{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Hyperbolic plane $\\mathbb{H}^2$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*This worksheet illustrates some features of [SageManifolds](http://sagemanifolds.obspm.fr/) (v1.0, as included in SageMath 7.5) on computations regarding the hyperbolic plane.*\n", "\n", "Click [here](https://raw.githubusercontent.com/sagemanifolds/SageManifolds/master/Worksheets/v1.0/SM_hyperbolic_plane.ipynb) to download the worksheet file (ipynb format). To run it, you must start SageMath with the Jupyter notebook, via the command `sage -n jupyter`" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*NB:* a version of SageMath at least equal to 7.5 is required to run this worksheet:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "'SageMath version 7.5, Release Date: 2017-01-11'" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "version()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First we set up the notebook to display mathematical objects using LaTeX formatting:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%display latex" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We also define a viewer for 3D plots (use `'threejs'` or `'jmol'` for interactive 3D graphics):" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "viewer3D = 'threejs' # must be 'threejs', jmol', 'tachyon' or None (default)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We declare $\\mathbb{H}^2$ as a 2-dimensional differentiable manifold:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2-dimensional differentiable manifold H2\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathbb{H}^2$ " ], "text/plain": [ "2-dimensional differentiable manifold H2" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "H2 = Manifold(2, 'H2', latex_name=r'\\mathbb{H}^2', start_index=1)\n", "print(H2)\n", "H2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We shall introduce charts on $\\mathbb{H}^2$ that are related to various models of the hyperbolic plane as submanifolds of $\\mathbb{R}^3$. Therefore, we start by declaring $\\mathbb{R}^3$ as a 3-dimensional manifold equiped with a global chart: the chart of Cartesian coordinates $(X,Y,Z)$:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\mathbb{R}^3,(X, Y, Z)\\right)$ " ], "text/plain": [ "Chart (R3, (X, Y, Z))" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R3 = Manifold(3, 'R3', latex_name=r'\\mathbb{R}^3', start_index=1)\n", "X3. = R3.chart()\n", "X3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Hyperboloid model\n", "\n", "The first chart we introduce is related to the **hyperboloid model of $\\mathbb{H}^2$**, namely to the representation of $\\mathbb{H}^2$ as the upper sheet ($Z>0$) of the hyperboloid of two sheets defined in $\\mathbb{R}^3$ by the equation $X^2 + Y^2 - Z^2 = -1$:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\mathbb{H}^2,(X, Y)\\right)$ " ], "text/plain": [ "Chart (H2, (X, Y))" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_hyp. = H2.chart()\n", "X_hyp" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The corresponding embedding of $\\mathbb{H}^2$ in $\\mathbb{R}^3$ is" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} \\Phi_1:& \\mathbb{H}^2 & \\longrightarrow & \\mathbb{R}^3 \\\\ & \\left(X, Y\\right) & \\longmapsto & \\left(X, Y, Z\\right) = \\left(X, Y, \\sqrt{X^{2} + Y^{2} + 1}\\right) \\end{array}$ " ], "text/plain": [ "Phi_1: H2 --> R3\n", " (X, Y) |--> (X, Y, Z) = (X, Y, sqrt(X^2 + Y^2 + 1))" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi1 = H2.diff_map(R3, [X, Y, sqrt(1+X^2+Y^2)], name='Phi_1', latex_name=r'\\Phi_1')\n", "Phi1.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By plotting the chart $\\left(\\mathbb{H}^2,(X,Y)\\right)$ in terms of the Cartesian coordinates of $\\mathbb{R}^3$, we get a graphical view of $\\Phi_1(\\mathbb{H}^2)$:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(X_hyp.plot(X3, mapping=Phi1, number_values=15, color='blue'), aspect_ratio=1, \n", " viewer=viewer3D, figsize=7)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "A second chart is obtained from the polar coordinates $(r,\\varphi)$ associated with $(X,Y)$. Contrary to $(X,Y)$, the polar chart is not defined on the whole $\\mathbb{H}^2$, but on the complement $U$ of the segment $\\{Y=0, x\\geq 0\\}$: " ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Open subset U of the 2-dimensional differentiable manifold H2\n" ] } ], "source": [ "U = H2.open_subset('U', coord_def={X_hyp: (Y!=0, X<0)})\n", "print(U)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that (y!=0, x<0) stands for $y\\not=0$ OR $x<0$; the condition $y\\not=0$ AND $x<0$ would have been written [y!=0, x<0] instead." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(U,(r, {\\varphi})\\right)$ " ], "text/plain": [ "Chart (U, (r, ph))" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_pol. = U.chart(r'r:(0,+oo) ph:(0,2*pi):\\varphi')\n", "X_pol" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}r :\\ \\left( 0 , +\\infty \\right) ;\\quad {\\varphi} :\\ \\left( 0 , 2 \\, \\pi \\right)$ " ], "text/plain": [ "r: (0, +oo); ph: (0, 2*pi)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_pol.coord_range()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We specify the transition map between the charts $\\left(U,(r,\\varphi)\\right)$ and $\\left(\\mathbb{H}^2,(X,Y)\\right)$ as $X=r\\cos\\varphi$, $Y=r\\sin\\varphi$:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(U,(r, {\\varphi})\\right) \\rightarrow \\left(U,(X, Y)\\right)$ " ], "text/plain": [ "Change of coordinates from Chart (U, (r, ph)) to Chart (U, (X, Y))" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pol_to_hyp = X_pol.transition_map(X_hyp, [r*cos(ph), r*sin(ph)])\n", "pol_to_hyp" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} X & = & r \\cos\\left({\\varphi}\\right) \\\\ Y & = & r \\sin\\left({\\varphi}\\right) \\end{array}\\right.$ " ], "text/plain": [ "X = r*cos(ph)\n", "Y = r*sin(ph)" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pol_to_hyp.display()" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [], "source": [ "pol_to_hyp.set_inverse(sqrt(X^2+Y^2), atan2(Y, X)) " ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} r & = & \\sqrt{X^{2} + Y^{2}} \\\\ {\\varphi} & = & \\arctan\\left(Y, X\\right) \\end{array}\\right.$ " ], "text/plain": [ "r = sqrt(X^2 + Y^2)\n", "ph = arctan2(Y, X)" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pol_to_hyp.inverse().display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The restriction of the embedding $\\Phi_1$ to $U$ has then two coordinate expressions:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} \\Phi_1:& U & \\longrightarrow & \\mathbb{R}^3 \\\\ & \\left(X, Y\\right) & \\longmapsto & \\left(X, Y, Z\\right) = \\left(X, Y, \\sqrt{X^{2} + Y^{2} + 1}\\right) \\\\ & \\left(r, {\\varphi}\\right) & \\longmapsto & \\left(X, Y, Z\\right) = \\left(r \\cos\\left({\\varphi}\\right), r \\sin\\left({\\varphi}\\right), \\sqrt{r^{2} + 1}\\right) \\end{array}$ " ], "text/plain": [ "Phi_1: U --> R3\n", " (X, Y) |--> (X, Y, Z) = (X, Y, sqrt(X^2 + Y^2 + 1))\n", " (r, ph) |--> (X, Y, Z) = (r*cos(ph), r*sin(ph), sqrt(r^2 + 1))" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi1.restrict(U).display()" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_hyp = X_pol.plot(X3, mapping=Phi1.restrict(U), number_values=15, ranges={r: (0,3)}, \n", " color='blue')\n", "show(graph_hyp, aspect_ratio=1, viewer=viewer3D, figsize=7)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\left(\\left(\\mathbb{H}^2,(X, Y)\\right), \\left(\\mathbb{R}^3,(X, Y, Z)\\right)\\right) : \\left(X, Y, \\sqrt{X^{2} + Y^{2} + 1}\\right)\\right\\}$ " ], "text/plain": [ "{(Chart (H2, (X, Y)),\n", " Chart (R3, (X, Y, Z))): Coordinate functions (X, Y, sqrt(X^2 + Y^2 + 1)) on the Chart (H2, (X, Y))}" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi1._coord_expression" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Metric and curvature\n", "\n", "The metric on $\\mathbb{H}^2$ is that induced by the Minkowksy metric on $\\mathbb{R}^3$: \n", "$$ \\eta = \\mathrm{d}X\\otimes\\mathrm{d}X + \\mathrm{d}Y\\otimes\\mathrm{d}Y\n", " - \\mathrm{d}Z\\otimes\\mathrm{d}Z $$" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\eta = \\mathrm{d} X\\otimes \\mathrm{d} X+\\mathrm{d} Y\\otimes \\mathrm{d} Y-\\mathrm{d} Z\\otimes \\mathrm{d} Z$ " ], "text/plain": [ "eta = dX*dX + dY*dY - dZ*dZ" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eta = R3.lorentzian_metric('eta', latex_name=r'\\eta')\n", "eta[1,1] = 1 ; eta[2,2] = 1 ; eta[3,3] = -1\n", "eta.display()" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = \\left( \\frac{Y^{2} + 1}{X^{2} + Y^{2} + 1} \\right) \\mathrm{d} X\\otimes \\mathrm{d} X + \\left( -\\frac{X Y}{X^{2} + Y^{2} + 1} \\right) \\mathrm{d} X\\otimes \\mathrm{d} Y + \\left( -\\frac{X Y}{X^{2} + Y^{2} + 1} \\right) \\mathrm{d} Y\\otimes \\mathrm{d} X + \\left( \\frac{X^{2} + 1}{X^{2} + Y^{2} + 1} \\right) \\mathrm{d} Y\\otimes \\mathrm{d} Y$ " ], "text/plain": [ "g = (Y^2 + 1)/(X^2 + Y^2 + 1) dX*dX - X*Y/(X^2 + Y^2 + 1) dX*dY - X*Y/(X^2 + Y^2 + 1) dY*dX + (X^2 + 1)/(X^2 + Y^2 + 1) dY*dY" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g = H2.metric('g')\n", "g.set( Phi1.pullback(eta) )\n", "g.display() " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The expression of the metric tensor in terms of the polar coordinates is" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = \\left( \\frac{1}{r^{2} + 1} \\right) \\mathrm{d} r\\otimes \\mathrm{d} r + r^{2} \\mathrm{d} {\\varphi}\\otimes \\mathrm{d} {\\varphi}$ " ], "text/plain": [ "g = 1/(r^2 + 1) dr*dr + r^2 dph*dph" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display(X_pol.frame(), X_pol)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Riemann curvature tensor associated with $g$ is" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tensor field Riem(g) of type (1,3) on the 2-dimensional differentiable manifold H2\n" ] } ], "source": [ "Riem = g.riemann()\n", "print(Riem)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{Riem}\\left(g\\right) = -r^{2} \\frac{\\partial}{\\partial r }\\otimes \\mathrm{d} {\\varphi}\\otimes \\mathrm{d} r\\otimes \\mathrm{d} {\\varphi} + r^{2} \\frac{\\partial}{\\partial r }\\otimes \\mathrm{d} {\\varphi}\\otimes \\mathrm{d} {\\varphi}\\otimes \\mathrm{d} r + \\left( \\frac{1}{r^{2} + 1} \\right) \\frac{\\partial}{\\partial {\\varphi} }\\otimes \\mathrm{d} r\\otimes \\mathrm{d} r\\otimes \\mathrm{d} {\\varphi} + \\left( -\\frac{1}{r^{2} + 1} \\right) \\frac{\\partial}{\\partial {\\varphi} }\\otimes \\mathrm{d} r\\otimes \\mathrm{d} {\\varphi}\\otimes \\mathrm{d} r$ " ], "text/plain": [ "Riem(g) = -r^2 d/dr*dph*dr*dph + r^2 d/dr*dph*dph*dr + 1/(r^2 + 1) d/dph*dr*dr*dph - 1/(r^2 + 1) d/dph*dr*dph*dr" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Riem.display(X_pol.frame(), X_pol)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Ricci tensor and the Ricci scalar:" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Field of symmetric bilinear forms Ric(g) on the 2-dimensional differentiable manifold H2\n" ] } ], "source": [ "Ric = g.ricci()\n", "print(Ric)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{Ric}\\left(g\\right) = \\left( -\\frac{1}{r^{2} + 1} \\right) \\mathrm{d} r\\otimes \\mathrm{d} r -r^{2} \\mathrm{d} {\\varphi}\\otimes \\mathrm{d} {\\varphi}$ " ], "text/plain": [ "Ric(g) = -1/(r^2 + 1) dr*dr - r^2 dph*dph" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Ric.display(X_pol.frame(), X_pol)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Scalar field r(g) on the 2-dimensional differentiable manifold H2\n" ] } ], "source": [ "Rscal = g.ricci_scalar()\n", "print(Rscal)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} \\mathrm{r}\\left(g\\right):& \\mathbb{H}^2 & \\longrightarrow & \\mathbb{R} \\\\ & \\left(X, Y\\right) & \\longmapsto & -2 \\\\ \\mbox{on}\\ U : & \\left(r, {\\varphi}\\right) & \\longmapsto & -2 \\end{array}$ " ], "text/plain": [ "r(g): H2 --> R\n", " (X, Y) |--> -2\n", "on U: (r, ph) |--> -2" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Rscal.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Hence we recover the fact that $(\\mathbb{H}^2,g)$ is a space of **constant negative curvature**." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In dimension 2, the Riemann curvature tensor is entirely determined by the Ricci scalar $R$ according to\n", "\n", "$$R^i_{\\ \\, jlk} = \\frac{R}{2} \\left( \\delta^i_{\\ \\, k} g_{jl} - \\delta^i_{\\ \\, l} g_{jk} \\right)$$\n", "\n", "Let us check this formula here, under the form $R^i_{\\ \\, jlk} = -R g_{j[k} \\delta^i_{\\ \\, l]}$:" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "delta = H2.tangent_identity_field()\n", "Riem == - Rscal*(g*delta).antisymmetrize(2,3) # 2,3 = last positions of the type-(1,3) tensor g*delta " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Similarly the relation $\\mathrm{Ric} = (R/2)\\; g$ must hold:" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Ric == (Rscal/2)*g" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Poincaré disk model\n", "\n", "The Poincaré disk model of $\\mathbb{H}^2$ is obtained by stereographic projection from the point $S=(0,0,-1)$ of the hyperboloid model to the plane $Z=0$. The radial coordinate $R$ of the image of a point of polar coordinate $(r,\\varphi)$ is\n", "$$ R = \\frac{r}{1+\\sqrt{1+r^2}}.$$\n", "Hence we define the Poincaré disk chart on $\\mathbb{H}^2$ by" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(U,(R, {\\varphi})\\right)$ " ], "text/plain": [ "Chart (U, (R, ph))" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_Pdisk. = U.chart(r'R:(0,1) ph:(0,2*pi):\\varphi')\n", "X_Pdisk" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}R :\\ \\left( 0 , 1 \\right) ;\\quad {\\varphi} :\\ \\left( 0 , 2 \\, \\pi \\right)$ " ], "text/plain": [ "R: (0, 1); ph: (0, 2*pi)" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_Pdisk.coord_range()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "and relate it to the hyperboloid polar chart by" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(U,(r, {\\varphi})\\right) \\rightarrow \\left(U,(R, {\\varphi})\\right)$ " ], "text/plain": [ "Change of coordinates from Chart (U, (r, ph)) to Chart (U, (R, ph))" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pol_to_Pdisk = X_pol.transition_map(X_Pdisk, [r/(1+sqrt(1+r^2)), ph])\n", "pol_to_Pdisk" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} R & = & \\frac{r}{\\sqrt{r^{2} + 1} + 1} \\\\ {\\varphi} & = & {\\varphi} \\end{array}\\right.$ " ], "text/plain": [ "R = r/(sqrt(r^2 + 1) + 1)\n", "ph = ph" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pol_to_Pdisk.display()" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} r & = & -\\frac{2 \\, R}{R^{2} - 1} \\\\ {\\varphi} & = & {\\varphi} \\end{array}\\right.$ " ], "text/plain": [ "r = -2*R/(R^2 - 1)\n", "ph = ph" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pol_to_Pdisk.set_inverse(2*R/(1-R^2), ph)\n", "pol_to_Pdisk.inverse().display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A view of the Poincaré disk chart via the embedding $\\Phi_1$:" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(X_Pdisk.plot(X3, mapping=Phi1.restrict(U), ranges={R: (0,0.9)}, color='blue',\n", " number_values=15), aspect_ratio=1, viewer=viewer3D, figsize=7)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The expression of the metric tensor in terms of coordinates $(R,\\varphi)$:" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = \\left( \\frac{4}{R^{4} - 2 \\, R^{2} + 1} \\right) \\mathrm{d} R\\otimes \\mathrm{d} R + \\left( \\frac{4 \\, R^{2}}{R^{4} - 2 \\, R^{2} + 1} \\right) \\mathrm{d} {\\varphi}\\otimes \\mathrm{d} {\\varphi}$ " ], "text/plain": [ "g = 4/(R^4 - 2*R^2 + 1) dR*dR + 4*R^2/(R^4 - 2*R^2 + 1) dph*dph" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display(X_Pdisk.frame(), X_Pdisk)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We may factorize each metric component:" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = \\frac{4}{{\\left(R + 1\\right)}^{2} {\\left(R - 1\\right)}^{2}} \\mathrm{d} R\\otimes \\mathrm{d} R + \\frac{4 \\, R^{2}}{{\\left(R + 1\\right)}^{2} {\\left(R - 1\\right)}^{2}} \\mathrm{d} {\\varphi}\\otimes \\mathrm{d} {\\varphi}$ " ], "text/plain": [ "g = 4/((R + 1)^2*(R - 1)^2) dR*dR + 4*R^2/((R + 1)^2*(R - 1)^2) dph*dph" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "for i in [1,2]:\n", " g[X_Pdisk.frame(), i, i, X_Pdisk].factor()\n", "g.display(X_Pdisk.frame(), X_Pdisk)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Cartesian coordinates on the Poincaré disk\n", "\n", "Let us introduce Cartesian coordinates $(u,v)$ on the Poincaré disk; since the latter has a unit radius, this amounts to define the following chart on $\\mathbb{H}^2$:" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\mathbb{H}^2,(u, v)\\right)$ " ], "text/plain": [ "Chart (H2, (u, v))" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_Pdisk_cart. = H2.chart('u:(-1,1) v:(-1,1)')\n", "X_Pdisk_cart.add_restrictions(u^2+v^2 < 1)\n", "X_Pdisk_cart" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On $U$, the Cartesian coordinates $(u,v)$ are related to the polar coordinates $(R,\\varphi)$ by the standard formulas:" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(U,(R, {\\varphi})\\right) \\rightarrow \\left(U,(u, v)\\right)$ " ], "text/plain": [ "Change of coordinates from Chart (U, (R, ph)) to Chart (U, (u, v))" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Pdisk_to_Pdisk_cart = X_Pdisk.transition_map(X_Pdisk_cart, [R*cos(ph), R*sin(ph)])\n", "Pdisk_to_Pdisk_cart" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} u & = & R \\cos\\left({\\varphi}\\right) \\\\ v & = & R \\sin\\left({\\varphi}\\right) \\end{array}\\right.$ " ], "text/plain": [ "u = R*cos(ph)\n", "v = R*sin(ph)" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Pdisk_to_Pdisk_cart.display()" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} R & = & \\sqrt{u^{2} + v^{2}} \\\\ {\\varphi} & = & \\arctan\\left(v, u\\right) \\end{array}\\right.$ " ], "text/plain": [ "R = sqrt(u^2 + v^2)\n", "ph = arctan2(v, u)" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Pdisk_to_Pdisk_cart.set_inverse(sqrt(u^2+v^2), atan2(v, u)) \n", "Pdisk_to_Pdisk_cart.inverse().display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The embedding of $\\mathbb{H}^2$ in $\\mathbb{R}^3$ associated with the Poincaré disk model is naturally defined as" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} \\Phi_2:& \\mathbb{H}^2 & \\longrightarrow & \\mathbb{R}^3 \\\\ & \\left(u, v\\right) & \\longmapsto & \\left(X, Y, Z\\right) = \\left(u, v, 0\\right) \\end{array}$ " ], "text/plain": [ "Phi_2: H2 --> R3\n", " (u, v) |--> (X, Y, Z) = (u, v, 0)" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi2 = H2.diff_map(R3, {(X_Pdisk_cart, X3): [u, v, 0]},\n", " name='Phi_2', latex_name=r'\\Phi_2')\n", "Phi2.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us use it to draw the Poincaré disk in $\\mathbb{R}^3$:" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_disk_uv = X_Pdisk_cart.plot(X3, mapping=Phi2, number_values=15)\n", "show(graph_disk_uv, viewer=viewer3D, figsize=7)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On $U$, the change of coordinates $(r,\\varphi) \\rightarrow (u,v)$ is obtained by combining the changes $(r,\\varphi) \\rightarrow (R,\\varphi)$ and $(R,\\varphi) \\rightarrow (u,v)$:" ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(U,(r, {\\varphi})\\right) \\rightarrow \\left(U,(u, v)\\right)$ " ], "text/plain": [ "Change of coordinates from Chart (U, (r, ph)) to Chart (U, (u, v))" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pol_to_Pdisk_cart = Pdisk_to_Pdisk_cart * pol_to_Pdisk\n", "pol_to_Pdisk_cart" ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} u & = & \\frac{r \\cos\\left({\\varphi}\\right)}{\\sqrt{r^{2} + 1} + 1} \\\\ v & = & \\frac{r \\sin\\left({\\varphi}\\right)}{\\sqrt{r^{2} + 1} + 1} \\end{array}\\right.$ " ], "text/plain": [ "u = r*cos(ph)/(sqrt(r^2 + 1) + 1)\n", "v = r*sin(ph)/(sqrt(r^2 + 1) + 1)" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pol_to_Pdisk_cart.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Still on $U$, the change of coordinates $(X,Y) \\rightarrow (u,v)$ is obtained by combining the changes $(X,Y) \\rightarrow (r,\\varphi)$ with $(r,\\varphi) \\rightarrow (u,v)$:" ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(U,(X, Y)\\right) \\rightarrow \\left(U,(u, v)\\right)$ " ], "text/plain": [ "Change of coordinates from Chart (U, (X, Y)) to Chart (U, (u, v))" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "hyp_to_Pdisk_cart_U = pol_to_Pdisk_cart * pol_to_hyp.inverse()\n", "hyp_to_Pdisk_cart_U" ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} u & = & \\frac{X}{\\sqrt{X^{2} + Y^{2} + 1} + 1} \\\\ v & = & \\frac{Y}{\\sqrt{X^{2} + Y^{2} + 1} + 1} \\end{array}\\right.$ " ], "text/plain": [ "u = X/(sqrt(X^2 + Y^2 + 1) + 1)\n", "v = Y/(sqrt(X^2 + Y^2 + 1) + 1)" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "hyp_to_Pdisk_cart_U.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We use the above expression to extend the change of coordinates $(X,Y) \\rightarrow (u,v)$ from $U$ to the whole manifold $\\mathbb{H}^2$:" ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\mathbb{H}^2,(X, Y)\\right) \\rightarrow \\left(\\mathbb{H}^2,(u, v)\\right)$ " ], "text/plain": [ "Change of coordinates from Chart (H2, (X, Y)) to Chart (H2, (u, v))" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "hyp_to_Pdisk_cart = X_hyp.transition_map(X_Pdisk_cart, hyp_to_Pdisk_cart_U(X,Y))\n", "hyp_to_Pdisk_cart" ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} u & = & \\frac{X}{\\sqrt{X^{2} + Y^{2} + 1} + 1} \\\\ v & = & \\frac{Y}{\\sqrt{X^{2} + Y^{2} + 1} + 1} \\end{array}\\right.$ " ], "text/plain": [ "u = X/(sqrt(X^2 + Y^2 + 1) + 1)\n", "v = Y/(sqrt(X^2 + Y^2 + 1) + 1)" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "hyp_to_Pdisk_cart.display()" ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} X & = & -\\frac{2 \\, u}{u^{2} + v^{2} - 1} \\\\ Y & = & -\\frac{2 \\, v}{u^{2} + v^{2} - 1} \\end{array}\\right.$ " ], "text/plain": [ "X = -2*u/(u^2 + v^2 - 1)\n", "Y = -2*v/(u^2 + v^2 - 1)" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "hyp_to_Pdisk_cart.set_inverse(2*u/(1-u^2-v^2), 2*v/(1-u^2-v^2))\n", "hyp_to_Pdisk_cart.inverse().display()" ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_Pdisk = X_pol.plot(X3, mapping=Phi2.restrict(U), ranges={r: (0, 20)}, number_values=15, \n", " label_axes=False)\n", "show(graph_hyp + graph_Pdisk, aspect_ratio=1, viewer=viewer3D, figsize=7)" ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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fdeAA3te2LY739GlcU2FhEDqnT+Oakdehnx/RqFFEU6YQjRjBKfYMUwewAGIaB6WlRN9/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by9BeG992z7DlwIjk+A7t3DhfT3RzkoXcx+/VDaPmsWND83b6LyifKoZHL477/4nfQ7Q4cij+vr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wMJs/HyTnxRfxWc+eEE77+AjuLyV6JTeE8wgQF2kRwd+bnIybsGNHaGG6d4ewa8MGbHP0KML3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\npas3Mkxj1KKF/XP3l1/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9OiF79hCyZQsh33yD9eaddwh5911Cli3DupSZifGh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j8fRkmnAwnKzSUaORLpv3l52L7NBkOVm0t0yy0weA0Ncpnly+Gl8pYZ5nDA2ApC9MMPIHAh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\nj/EAAAAASUVORK5CYII=\n", "text/plain": [ "Graphics object consisting of 30 graphics primitives" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_pol.plot(X_Pdisk_cart, ranges={r: (0, 20)}, number_values=15)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Metric tensor in Poincaré disk coordinates $(u,v)$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From now on, we are using the Poincaré disk chart $(\\mathbb{H}^2,(u,v))$ as the default one on $\\mathbb{H}^2$:" ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "collapsed": true }, "outputs": [], "source": [ "H2.set_default_chart(X_Pdisk_cart)\n", "H2.set_default_frame(X_Pdisk_cart.frame())" ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = \\left( \\frac{u^{4} + v^{4} + 2 \\, {\\left(u^{2} + 1\\right)} v^{2} - 2 \\, u^{2} + 1}{u^{4} + v^{4} + 2 \\, {\\left(u^{2} + 1\\right)} v^{2} + 2 \\, u^{2} + 1} \\right) \\mathrm{d} X\\otimes \\mathrm{d} X + \\left( -\\frac{4 \\, u v}{u^{4} + v^{4} + 2 \\, {\\left(u^{2} + 1\\right)} v^{2} + 2 \\, u^{2} + 1} \\right) \\mathrm{d} X\\otimes \\mathrm{d} Y + \\left( -\\frac{4 \\, u v}{u^{4} + v^{4} + 2 \\, {\\left(u^{2} + 1\\right)} v^{2} + 2 \\, u^{2} + 1} \\right) \\mathrm{d} Y\\otimes \\mathrm{d} X + \\left( \\frac{u^{4} + v^{4} + 2 \\, {\\left(u^{2} - 1\\right)} v^{2} + 2 \\, u^{2} + 1}{u^{4} + v^{4} + 2 \\, {\\left(u^{2} + 1\\right)} v^{2} + 2 \\, u^{2} + 1} \\right) \\mathrm{d} Y\\otimes \\mathrm{d} Y$ " ], "text/plain": [ "g = (u^4 + v^4 + 2*(u^2 + 1)*v^2 - 2*u^2 + 1)/(u^4 + v^4 + 2*(u^2 + 1)*v^2 + 2*u^2 + 1) dX*dX - 4*u*v/(u^4 + v^4 + 2*(u^2 + 1)*v^2 + 2*u^2 + 1) dX*dY - 4*u*v/(u^4 + v^4 + 2*(u^2 + 1)*v^2 + 2*u^2 + 1) dY*dX + (u^4 + v^4 + 2*(u^2 - 1)*v^2 + 2*u^2 + 1)/(u^4 + v^4 + 2*(u^2 + 1)*v^2 + 2*u^2 + 1) dY*dY" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display(X_hyp.frame())" ] }, { "cell_type": "code", "execution_count": 55, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = \\left( \\frac{4}{u^{4} + v^{4} + 2 \\, {\\left(u^{2} - 1\\right)} v^{2} - 2 \\, u^{2} + 1} \\right) \\mathrm{d} u\\otimes \\mathrm{d} u + \\left( \\frac{4}{u^{4} + v^{4} + 2 \\, {\\left(u^{2} - 1\\right)} v^{2} - 2 \\, u^{2} + 1} \\right) \\mathrm{d} v\\otimes \\mathrm{d} v$ " ], "text/plain": [ "g = 4/(u^4 + v^4 + 2*(u^2 - 1)*v^2 - 2*u^2 + 1) du*du + 4/(u^4 + v^4 + 2*(u^2 - 1)*v^2 - 2*u^2 + 1) dv*dv" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display()" ] }, { "cell_type": "code", "execution_count": 56, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = \\frac{4}{{\\left(u^{2} + v^{2} - 1\\right)}^{2}} \\mathrm{d} u\\otimes \\mathrm{d} u + \\frac{4}{{\\left(u^{2} + v^{2} - 1\\right)}^{2}} \\mathrm{d} v\\otimes \\mathrm{d} v$ " ], "text/plain": [ "g = 4/(u^2 + v^2 - 1)^2 du*du + 4/(u^2 + v^2 - 1)^2 dv*dv" ] }, "execution_count": 56, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g[1,1].factor() ; g[2,2].factor()\n", "g.display()" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "## Hemispherical model\n", "\n", "The **hemispherical model of $\\mathbb{H}^2$** is obtained by the inverse stereographic projection from the point $S = (0,0,-1)$ of the Poincaré disk to the unit sphere $X^2+Y^2+Z^2=1$. This induces a spherical coordinate chart on $U$:" ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(U,({\\theta}, {\\varphi})\\right)$ " ], "text/plain": [ "Chart (U, (th, ph))" ] }, "execution_count": 57, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_spher. = U.chart(r'th:(0,pi/2):\\theta ph:(0,2*pi):\\varphi')\n", "X_spher" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From the stereographic projection from $S$, we obtain that\n", "\\begin{equation}\n", "\\sin\\theta = \\frac{2R}{1+R^2}\n", "\\end{equation}\n", "Hence the transition map:" ] }, { "cell_type": "code", "execution_count": 58, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(U,(R, {\\varphi})\\right) \\rightarrow \\left(U,({\\theta}, {\\varphi})\\right)$ " ], "text/plain": [ "Change of coordinates from Chart (U, (R, ph)) to Chart (U, (th, ph))" ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Pdisk_to_spher = X_Pdisk.transition_map(X_spher, [arcsin(2*R/(1+R^2)), ph])\n", "Pdisk_to_spher" ] }, { "cell_type": "code", "execution_count": 59, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} {\\theta} & = & \\arcsin\\left(\\frac{2 \\, R}{R^{2} + 1}\\right) \\\\ {\\varphi} & = & {\\varphi} \\end{array}\\right.$ " ], "text/plain": [ "th = arcsin(2*R/(R^2 + 1))\n", "ph = ph" ] }, "execution_count": 59, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Pdisk_to_spher.display()" ] }, { "cell_type": "code", "execution_count": 60, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} R & = & \\frac{\\sin\\left({\\theta}\\right)}{\\cos\\left({\\theta}\\right) + 1} \\\\ {\\varphi} & = & {\\varphi} \\end{array}\\right.$ " ], "text/plain": [ "R = sin(th)/(cos(th) + 1)\n", "ph = ph" ] }, "execution_count": 60, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Pdisk_to_spher.set_inverse(sin(th)/(1+cos(th)), ph)\n", "Pdisk_to_spher.inverse().display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the spherical coordinates $(\\theta,\\varphi)$, the metric takes the following form:" ] }, { "cell_type": "code", "execution_count": 61, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = \\frac{1}{\\cos\\left({\\theta}\\right)^{2}} \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\frac{\\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\theta}\\right)^{2}} \\mathrm{d} {\\varphi}\\otimes \\mathrm{d} {\\varphi}$ " ], "text/plain": [ "g = cos(th)^(-2) dth*dth + sin(th)^2/cos(th)^2 dph*dph" ] }, "execution_count": 61, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display(X_spher.frame(), X_spher)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The embedding of $\\mathbb{H}^2$ in $\\mathbb{R}^3$ associated with the hemispherical model is naturally:" ] }, { "cell_type": "code", "execution_count": 62, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} \\Phi_3:& \\mathbb{H}^2 & \\longrightarrow & \\mathbb{R}^3 \\\\ \\mbox{on}\\ U : & \\left(R, {\\varphi}\\right) & \\longmapsto & \\left(X, Y, Z\\right) = \\left(\\frac{2 \\, R \\cos\\left({\\varphi}\\right)}{R^{2} + 1}, \\frac{2 \\, R \\sin\\left({\\varphi}\\right)}{R^{2} + 1}, -\\frac{R^{2} - 1}{R^{2} + 1}\\right) \\\\ \\mbox{on}\\ U : & \\left({\\theta}, {\\varphi}\\right) & \\longmapsto & \\left(X, Y, Z\\right) = \\left(\\cos\\left({\\varphi}\\right) \\sin\\left({\\theta}\\right), \\sin\\left({\\varphi}\\right) \\sin\\left({\\theta}\\right), \\cos\\left({\\theta}\\right)\\right) \\end{array}$ " ], "text/plain": [ "Phi_3: H2 --> R3\n", "on U: (R, ph) |--> (X, Y, Z) = (2*R*cos(ph)/(R^2 + 1), 2*R*sin(ph)/(R^2 + 1), -(R^2 - 1)/(R^2 + 1))\n", "on U: (th, ph) |--> (X, Y, Z) = (cos(ph)*sin(th), sin(ph)*sin(th), cos(th))" ] }, "execution_count": 62, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi3 = H2.diff_map(R3, {(X_spher, X3): [sin(th)*cos(ph), sin(th)*sin(ph), cos(th)]},\n", " name='Phi_3', latex_name=r'\\Phi_3')\n", "Phi3.display()" ] }, { "cell_type": "code", "execution_count": 63, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_spher = X_pol.plot(X3, mapping=Phi3, ranges={r: (0, 20)}, number_values=15, color='orange', \n", " label_axes=False)\n", "show(graph_hyp + graph_Pdisk + graph_spher, aspect_ratio=1, viewer=viewer3D, figsize=7)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Poincaré half-plane model\n", "\n", "The **Poincaré half-plane model of $\\mathbb{H}^2$** is obtained by stereographic projection from the point $W=(-1,0,0)$ of the hemispherical model to the plane $X=1$. This induces a new coordinate chart on $\\mathbb{H}^2$ by setting $(x,y)=(Y,Z)$ in the plane $X=1$:" ] }, { "cell_type": "code", "execution_count": 64, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\mathbb{H}^2,(x, y)\\right)$ " ], "text/plain": [ "Chart (H2, (x, y))" ] }, "execution_count": 64, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_hplane. = H2.chart('x y:(0,+oo)')\n", "X_hplane" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The coordinate transformation $(\\theta,\\varphi)\\rightarrow (x,y)$ is easily deduced from the stereographic projection from the point $W$:" ] }, { "cell_type": "code", "execution_count": 65, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(U,({\\theta}, {\\varphi})\\right) \\rightarrow \\left(U,(x, y)\\right)$ " ], "text/plain": [ "Change of coordinates from Chart (U, (th, ph)) to Chart (U, (x, y))" ] }, "execution_count": 65, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher_to_hplane = X_spher.transition_map(X_hplane, [2*sin(th)*sin(ph)/(1+sin(th)*cos(ph)),\n", " 2*cos(th)/(1+sin(th)*cos(ph))])\n", "spher_to_hplane" ] }, { "cell_type": "code", "execution_count": 66, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} x & = & \\frac{2 \\, \\sin\\left({\\varphi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\varphi}\\right) \\sin\\left({\\theta}\\right) + 1} \\\\ y & = & \\frac{2 \\, \\cos\\left({\\theta}\\right)}{\\cos\\left({\\varphi}\\right) \\sin\\left({\\theta}\\right) + 1} \\end{array}\\right.$ " ], "text/plain": [ "x = 2*sin(ph)*sin(th)/(cos(ph)*sin(th) + 1)\n", "y = 2*cos(th)/(cos(ph)*sin(th) + 1)" ] }, "execution_count": 66, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher_to_hplane.display()" ] }, { "cell_type": "code", "execution_count": 67, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(U,(R, {\\varphi})\\right) \\rightarrow \\left(U,(x, y)\\right)$ " ], "text/plain": [ "Change of coordinates from Chart (U, (R, ph)) to Chart (U, (x, y))" ] }, "execution_count": 67, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Pdisk_to_hplane = spher_to_hplane * Pdisk_to_spher\n", "Pdisk_to_hplane" ] }, { "cell_type": "code", "execution_count": 68, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} x & = & \\frac{4 \\, R \\sin\\left({\\varphi}\\right)}{R^{2} + 2 \\, R \\cos\\left({\\varphi}\\right) + 1} \\\\ y & = & -\\frac{2 \\, {\\left(R^{2} - 1\\right)}}{R^{2} + 2 \\, R \\cos\\left({\\varphi}\\right) + 1} \\end{array}\\right.$ " ], "text/plain": [ "x = 4*R*sin(ph)/(R^2 + 2*R*cos(ph) + 1)\n", "y = -2*(R^2 - 1)/(R^2 + 2*R*cos(ph) + 1)" ] }, "execution_count": 68, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Pdisk_to_hplane.display()" ] }, { "cell_type": "code", "execution_count": 69, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(U,(u, v)\\right) \\rightarrow \\left(U,(x, y)\\right)$ " ], "text/plain": [ "Change of coordinates from Chart (U, (u, v)) to Chart (U, (x, y))" ] }, "execution_count": 69, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Pdisk_cart_to_hplane_U = Pdisk_to_hplane * Pdisk_to_Pdisk_cart.inverse()\n", "Pdisk_cart_to_hplane_U" ] }, { "cell_type": "code", "execution_count": 70, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} x & = & \\frac{4 \\, v}{u^{2} + v^{2} + 2 \\, u + 1} \\\\ y & = & -\\frac{2 \\, {\\left(u^{2} + v^{2} - 1\\right)}}{u^{2} + v^{2} + 2 \\, u + 1} \\end{array}\\right.$ " ], "text/plain": [ "x = 4*v/(u^2 + v^2 + 2*u + 1)\n", "y = -2*(u^2 + v^2 - 1)/(u^2 + v^2 + 2*u + 1)" ] }, "execution_count": 70, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Pdisk_cart_to_hplane_U.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us use the above formula to define the transition map $(u,v)\\rightarrow (x,y)$ on the whole manifold $\\mathbb{H}^2$ (and not only on $U$):" ] }, { "cell_type": "code", "execution_count": 71, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\mathbb{H}^2,(u, v)\\right) \\rightarrow \\left(\\mathbb{H}^2,(x, y)\\right)$ " ], "text/plain": [ "Change of coordinates from Chart (H2, (u, v)) to Chart (H2, (x, y))" ] }, "execution_count": 71, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Pdisk_cart_to_hplane = X_Pdisk_cart.transition_map(X_hplane, Pdisk_cart_to_hplane_U(u,v))\n", "Pdisk_cart_to_hplane" ] }, { "cell_type": "code", "execution_count": 72, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} x & = & \\frac{4 \\, v}{u^{2} + v^{2} + 2 \\, u + 1} \\\\ y & = & -\\frac{2 \\, {\\left(u^{2} + v^{2} - 1\\right)}}{u^{2} + v^{2} + 2 \\, u + 1} \\end{array}\\right.$ " ], "text/plain": [ "x = 4*v/(u^2 + v^2 + 2*u + 1)\n", "y = -2*(u^2 + v^2 - 1)/(u^2 + v^2 + 2*u + 1)" ] }, "execution_count": 72, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Pdisk_cart_to_hplane.display()" ] }, { "cell_type": "code", "execution_count": 73, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} u & = & -\\frac{x^{2} + y^{2} - 4}{x^{2} + {\\left(y + 2\\right)}^{2}} \\\\ v & = & \\frac{4 \\, x}{x^{2} + {\\left(y + 2\\right)}^{2}} \\end{array}\\right.$ " ], "text/plain": [ "u = -(x^2 + y^2 - 4)/(x^2 + (y + 2)^2)\n", "v = 4*x/(x^2 + (y + 2)^2)" ] }, "execution_count": 73, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Pdisk_cart_to_hplane.set_inverse((4-x^2-y^2)/(x^2+(2+y)^2), 4*x/(x^2+(2+y)^2))\n", "Pdisk_cart_to_hplane.inverse().display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since the coordinates $(x,y)$ correspond to $(Y,Z)$ in the plane $X=1$, the embedding of $\\mathbb{H}^2$ in $\\mathbb{R}^3$ naturally associated with the Poincaré half-plane model is" ] }, { "cell_type": "code", "execution_count": 74, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} \\Phi_4:& \\mathbb{H}^2 & \\longrightarrow & \\mathbb{R}^3 \\\\ & \\left(u, v\\right) & \\longmapsto & \\left(X, Y, Z\\right) = \\left(1, \\frac{4 \\, v}{u^{2} + v^{2} + 2 \\, u + 1}, -\\frac{2 \\, {\\left(u^{2} + v^{2} - 1\\right)}}{u^{2} + v^{2} + 2 \\, u + 1}\\right) \\\\ & \\left(x, y\\right) & \\longmapsto & \\left(X, Y, Z\\right) = \\left(1, x, y\\right) \\end{array}$ " ], "text/plain": [ "Phi_4: H2 --> R3\n", " (u, v) |--> (X, Y, Z) = (1, 4*v/(u^2 + v^2 + 2*u + 1), -2*(u^2 + v^2 - 1)/(u^2 + v^2 + 2*u + 1))\n", " (x, y) |--> (X, Y, Z) = (1, x, y)" ] }, "execution_count": 74, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi4 = H2.diff_map(R3, {(X_hplane, X3): [1, x, y]}, name='Phi_4', latex_name=r'\\Phi_4')\n", "Phi4.display()" ] }, { "cell_type": "code", "execution_count": 75, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_hplane = X_pol.plot(X3, mapping=Phi4.restrict(U), ranges={r: (0, 1.5)}, number_values=15, \n", " color='brown', label_axes=False)\n", "show(graph_hyp + graph_Pdisk + graph_spher + graph_hplane, aspect_ratio=1, viewer=viewer3D,\n", " figsize=8)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us draw the grid of the hyperboloidal coordinates $(r,\\varphi)$ in terms of the half-plane coordinates $(x,y)$:" ] }, { "cell_type": "code", "execution_count": 76, "metadata": { "collapsed": true }, "outputs": [], "source": [ "pol_to_hplane = Pdisk_to_hplane * pol_to_Pdisk" ] }, { "cell_type": "code", "execution_count": 77, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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x8QEAREdHIzo6urGikoEpuHQJR2fNQvbx4/AfMQIdp07lhUCNjKTVQs6BPRJI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BAAAg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\nMDs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"text/plain": [ "Graphics object consisting of 30 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(X_pol.plot(X_hplane, ranges={r: (0,24)}, style={r: '-', ph: '--'}, number_values=15, \n", " plot_points=200, color='brown'), xmin=-5, xmax=5, ymin=0, ymax=5, aspect_ratio=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The solid curves are those along which $r$ varies while $\\varphi$ is kept constant. Conversely, the dashed curves are those along which $\\varphi$ varies, while $r$ is kept constant. We notice that the former curves are arcs of circles orthogonal to the half-plane boundary $y=0$, hence they are geodesics of $(\\mathbb{H}^2,g)$. This is not surprising since they correspond to the intersections of the hyperboloid with planes through the origin (namely the plane $\\varphi=\\mathrm{const}$). The point $(x,y) = (0,2)$ corresponds to $r=0$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We may also depict the Poincaré disk coordinates $(u,v)$ in terms of the half-plane coordinates $(x,y)$:" ] }, { "cell_type": "code", "execution_count": 78, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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2223atGmTnn/+eZ1//vlauXKlhoaGTvhnotHoxPf94OCg9u3b5+OMfTaalJ7d\n5Y0OGR0d1QUXXKB77rknkK/9JW94XrdunSRp3759cnL7UCrlBZ9UynomM+ab3/ym7rzzTl177bWS\npIceekiLFi3SY489ptWrV5/wz1VWVqqhocGvaQKYAVu2bNH69et10003SZLuvfdePf7443rggQd0\nxx13HPfPhEIhd773MxkpkfJGh6xatUqrVq2SpEC+9rPnBye1Z88eDQ4O6uqrr574WCQS0Xvf+17t\n2LHjpH/2D3/4g5qamnTOOedo3bp1eu2116Z/ggMD3mmnAX8aKwJl5+gxaW+/N06zsbEx7dy5M+/7\nPxQK6UMf+tBJv/9HRka0dOlSnXnmmfrIRz6i7lm8Mo5gIvzgpAYHBxUKhbRo0aK8jy9atEiDg4Mn\n/HMrVqzQD37wAz311FO69957tWfPHl1++eUaHR2d3gkODEibNrkbfpJJ6aWXvNFK7u90uv9upyqd\n8d5ySLv1m/eEY2Nee4NjY9P+0ENDQ0qn0wV9/7/rXe/SAw88oG3btunhhx9WJpPR+9///hnv/A0U\noqDw88Mf/lD19fWqr69XJBLRr3/965maF4y89e94bOz4P1Cz2exJ3+dduXKlrr/+erW1temaa67R\nz372Mx0+fFg//vGPZ2rqbiqH0369L+ePfuO0j+9O9v2/YsUKrVu3Tu95z3t02WWX6dFHH1VDQ4Pu\nv/9+n2cJnFhB4ee6667TCy+8oBdeeEG/+93vdNFFF83UvKbOgQ3Hfnrr3/GCBQuUzWZ14MCBvK97\n4403vN8Gp3j9o9Go3vnOd056Sixwcu01WlqsZwIrufYStbPvPlsLFixQOBw+8fe/NOmG38rKSl14\n4YWz73u/XDi64bpUBYWfuro6LVu2bOK/qqr8XjImO74d2HB8UtP84vvWv+PW1lYtXrxY27dvn/ia\neDyu//zP/9T73//+KV//kZERvfLKK2q0bMMwE3LtNbjBpLty7SVm4Q325syZo/b29rzv/2w2q+3b\nt3vf/9KkG34zmYx27do1c9/7szh8TomjG65LVfJpr8OHD+vVV19Vf3+/stmsent7lc1mtXjx4re9\nT4wZ4ENvq8997nP66le/qnPPPVdLly7VnXfeqSVLlui6667zgpekqz/zGV1/88269dZbJUm33367\nrr32Wp111lnq7+/Xhg0bVFlZqbVr187oXAFMry984Qv6xCc+ofb2dl1yySXasmWLEomEbr75ZknS\nTZ/+b1oMXFvuAAAdrUlEQVQSrtLXvvsdSdJXvvIVrVixQueee66OHDmif/iHf9C+fft0yy23zMwE\n6W1mYnR0VLt375446dXX16cXXnhB8+fP1xlnnGE8u8mVHH62bdumT37ykwqFQgqFQhMvbhs2bNBd\nd91V8gTLXjk0lpxhd9xxhxKJhNavX68jR47osssu0xNPPKG5c+dOfM2e11/Pu+/H/v379fGPf1wH\nDx5UQ0ODLr30Uv3mN7/RaaedZvEUABRp9erVGhoa0l133aUDBw7oggsu0FNPPTVxlH3/6/2qrItO\nfP3hw4f16U9/WoODgzr11FPV3t6uHTt2qLm52eopzCxHG+s+99xzuuqqqyZe+2+77TZJ0ic+8Qk9\n8MADxrObXPB7e9FbyZb19beub60Mnn/8F08r+sErFfuP/0+Rq67wfwKu99ayfv7W9V3H9S/K7HuT\nGm5xvas8QFdvoGAlv+0FmGpt9e5zA7iqrka6uM16FkCgEH6AIMud9lu2zG4Oze/MH/2WO+1TXTX5\n1wKAZsPbXg5sOC5rrl9/6/Ya5XDUvq4uf/Sb9VHzGWwvEQiObvgtG1z/ogR/w7PrBgak++6T1q93\nN4BYKoMNx9bi8bii0ahisZgikYj1dPzHhlNbR49JA29KjQ1S1dzJvx7QbFj5cZ3rva0AuG0Ge5th\n9iL8lKocGksCAGy43lg3oAg/pSqHxpJAGVizZo06OjrU2dlpPRXAPzTWDSROewGYFo888oibe34A\nBA4rPwi2KXaVB2YtunoDBSP8INim2FV+1rI+ai9J+/vzR7+5ftScrt5AwYIffthwbMv162/dXqMc\nTvsdeCN/9Jv1aR/X20uw4dcW178o07vnJ5GQenun9SEn1dMjrVsnbd3q3e3Wb7mNzlYbnvv6vLv7\n9vXZ1Hf9+kvS//gf3spTV5f/tcvh+b/6qjceHfPueeO33EZTyw2nzWd7Ky8uPv9EUurdKzUv9e62\n7bfkUal6rjdacPn611ZL4bC/NafJ9N7kMHfDNwDOiF9xtaJPb1fs8V8oUjfPejoA/BLgG3tO78pP\nc7N3p1s/lcPKg2V9a9bP37q+tXJ4/r9/SXp6u1Qx7v0w9Jv1yoM16+dvXd+a9fO3XvkJqOkNP7W1\ndrf4b2mxqf3HjSUt+ytZs7r+5VLfmuXzjw17Y9Uc298Ca2sC+1votLB+/tb1rdTWSBfVeY11rfrL\n5ebh4vUvEvf5KVWusSQAwD25xroIFEePJ2DWcL2rPEBXb6BgrPwg2BobvfvcuMr6qL0kVVXlj35z\n/ah51VxpaZP1LIBAIfwAQdba6t1nyVJba/7ot7oa6eI2m9oAAin4vyrlNhy7eNKnHLh+/WmvAdfb\nS9TWSBed5+ZJr3LA9S9K8MNPbsOxqyetrF98Xb/+rrfXAO0lcht+rU46uR4+ra9/QHG1go4XXwAu\ncz18oiiEn1KVQ2NJAIAN1xvrBhThp1Tl0FgSAGDDurEuikL4QbC53lUeoKs3UDDCD4Ktp0dqa7Pt\nag5YSiSl516y7WoPBAzhBwgy69N+krSrO3/0m+unfQAULPjhhw3Htly//tbtNcrhtN/Ro/mj36xP\n+7jeXoINv7a4/kWZHeHH5Q3H1i++XH8v/NFbzF259hJVc61nYsN6w6/r4dP6+gcU7S2CzvXeVgDc\nRm8zFCH4Kz/WyqGxJADAhuuNdQOKlZ9SlUNjSQCADRrrBhJRFcC0WPO3X1JHR4c6OzutpwIAJ8XK\nD4It11V+2TLrmTjvkbu/pshVV1hPwz25rt7VVdYzAQKD8INgy3WVd5X1aT9JWrQwf/Sb66d9cl29\nAUxZ8MMPG45tuX79k0mpr89beaoxeAEqh9N+S5ryR79Zn/ZJZ6TUUW/lJezgTgI2/Nri+hcllM1m\ns9aTQAmsX3xd19UltbdLO3dKy5dbz8ZEPB5XNBpVLBZTJBKxno7/hkelrh5peYtUX2c9G/e4Hj5R\nFP6lBB29rQC4jN5mKALhBwAAOIXwU6pyaCwJALBBY91AIvyUqhwaSwIAbFg31kVRCD8INte7ygN0\n9QYKRvhBsLneVT6Z9NqrJA2X3EdH80e/pTPeWw5pR3/zpqs3UDDCDxBk5XDar/fl/NFvnPYBUCD/\nbnKYSEi9vdP/uH190he/KG3ebNPiIPeiY/XiY13f9eufSkk//rE3dnX5X9/6+UvSq69649Ex7543\nfsuFHqvwk8lILcu80cXnnzwq7dkvnb1EqjFosWH9/K3rz/T1r62WwuHpf1xj/t3kMHczOACzSvyK\nqxV9ertij/9Ckbp51tMBMJ1m6c07/Vv5aW727oI73Xp6pHXrpK1bvSaXfrOub836+VvXt1YOz//3\nL0lPb5cqxr0flH5LJKXevVLzUq/Jp2usn791fWvWz3+m69fOztZF/oWf2tqZvf1/S4tNe4FcY8kP\nftC2uaQ1q+tfLvWtWT7/2LA3Vs2x/Q2xtmZW/oY6ZdbP37q+lVxj3VMiXp85K65e/yIFv7GptXJo\nLAkAsGHdWBdF4bQXgs31rvIAXb2BgrHyg2BrbfXucwO4qq5GurjNehZAoBB+gCBraZF27bK5zUBO\n8zvzR7/V1kgXnSdVGxyzBhBIwV8nzW04dnmzsSXXr791e42aGq+xbo3hKZu6uvzRb+EKb/UjbPTj\nzPX2ErkNv3PnWM/ETVz/ovh3nx/MjIEB6b77pPXr3Q0glnL3r9q509nTZvF4XNFoVLFYTJFIxHo6\n/hselbp6Zu39UMre0WPSwJtSY4PtaSsESvBXflznem8rAG6jtxmKQPgpVTk0lgQA2HC9sW5AEX5K\nVQ6NJQEANmisG0iEHwDTYs2aNero6FBnZ6f1VADgpDjqjmDr7pb+4i+kn/zEu+cPzDzyyCNubni2\nNpqUul+RWs/xTr0BmBQrPwi2VMoLQKmU9UxsWB+1l6T9/fmj31w/ap7JSImUNwKYkuCHHzYc23L9\n+lu31yiH034H3sgf/WZ92sf19hJs+LXF9S9K8L9bXd9wbP3i6/r1z7XX4C03d+XaS7j6lpP1hl/X\nw6f19Q8o9vwEHb2tALiM3mYogqNRGQAAuIqVn1KVQ2NJAIANGusGEuGnVLnGkgAA9+Qa6yJQeNsL\nweZ6V3mArt5AwVj5QbA1Nnr3uXGV9Wk/Saqqyh/95vppn6q50tIm61kAgUL4AYKsHE77tbXmj37j\ntA+AAgX/V6XchuOWFuuZuMn169/d7e356u62ngmsjCalZ3d5o4tyG35r2fdigutflOCHn9yG4xpH\n/+KtX3xdv/6ut9cA7SVyG37DRi8nrodP6+sfUFytoOPFF4DLXA+fKArhp1Tl0FgSAGDD9ca6AUX4\nKVU5NJYEANiwbqyLohB+EGyud5UH6OoNFIzwg2Bzvas8QFdvoGDleZ+fRELq7bWexdTkXnStXnyt\n61uzfv7W9fv6pC9+Udq82a6/XM/L3vhsl3TJxf7XTx6V9uyXzl4i1RjcaDEXOqzCh3V9a9bP37p+\nMWqrpXDYehamQtlsNms9ibfp6pLa261nAWAK4ldcrejT2xV7/BeK1M2zng6AySxvkerrrGdhqjxX\nfpqbpZ07p/a1PT3SunXS1q0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"text/plain": [ "Graphics object consisting of 64 graphics primitives" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_Pdisk_cart.plot(ranges={u: (-1, 0), v: (-1, 0)}, \n", " style={u: '-', v: '--'}) + \\\n", "X_Pdisk_cart.plot(ranges={u: (-1, 0), v: (0., 1)}, \n", " style={u: '-', v: '--'}, color='orange') + \\\n", "X_Pdisk_cart.plot(ranges={u: (0, 1), v: (-1, 0)}, \n", " style={u: '-', v: '--'}, color='pink') + \\\n", "X_Pdisk_cart.plot(ranges={u: (0, 1), v: (0, 1)}, \n", " style={u: '-', v: '--'}, color='violet')" ] }, { "cell_type": "code", "execution_count": 79, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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6Cz8/GDECXnxRBgcWKWIuS1ycHOBes0Ye27fLVqTQUGjZUgqd9HQtClxFrgLQ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\ny2ganJkPYYOvlg4NrC+a/kP2ydHgCZE8XdEHZteEk1NVRVwwF7fCgfe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avw6dpqiOQj3V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Ee7DfxNhikFiWIPpYlMSbCax2yQTpbYzoUChTYewycEzsn+RbMYvkGnEhOpIIaE4Nz5keij9V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\nxhbatnRSRsA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"text/plain": [ "Graphics object consisting of 64 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(X_Pdisk_cart.plot(X_hplane, ranges={u: (-1, 0), v: (-1, 0)}, \n", " style={u: '-', v: '--'}) + \\\n", " X_Pdisk_cart.plot(X_hplane, ranges={u: (-1, 0), v: (0, 1)}, \n", " style={u: '-', v: '--'}, color='orange') + \\\n", " X_Pdisk_cart.plot(X_hplane, ranges={u: (0, 1), v: (-1, 0)}, \n", " style={u: '-', v: '--'}, color='pink') + \\\n", " X_Pdisk_cart.plot(X_hplane, ranges={u: (0, 1), v: (0, 1)}, \n", " style={u: '-', v: '--'}, color='violet'),\n", " xmin=-5, xmax=5, ymin=0, ymax=5, aspect_ratio=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The expression of the metric tensor in the half-plane coordinates $(x,y)$ is" ] }, { "cell_type": "code", "execution_count": 80, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = \\frac{1}{y^{2}} \\mathrm{d} x\\otimes \\mathrm{d} x + \\frac{1}{y^{2}} \\mathrm{d} y\\otimes \\mathrm{d} y$ " ], "text/plain": [ "g = y^(-2) dx*dx + y^(-2) dy*dy" ] }, "execution_count": 80, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display(X_hplane.frame(), X_hplane)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "## Summary\n", "\n", "9 charts have been defined on $\\mathbb{H}^2$:" ] }, { "cell_type": "code", "execution_count": 81, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[\\left(\\mathbb{H}^2,(X, Y)\\right), \\left(U,(X, Y)\\right), \\left(U,(r, {\\varphi})\\right), \\left(U,(R, {\\varphi})\\right), \\left(\\mathbb{H}^2,(u, v)\\right), \\left(U,(u, v)\\right), \\left(U,({\\theta}, {\\varphi})\\right), \\left(\\mathbb{H}^2,(x, y)\\right), \\left(U,(x, y)\\right)\\right]$ " ], "text/plain": [ "[Chart (H2, (X, Y)),\n", " Chart (U, (X, Y)),\n", " Chart (U, (r, ph)),\n", " Chart (U, (R, ph)),\n", " Chart (H2, (u, v)),\n", " Chart (U, (u, v)),\n", " Chart (U, (th, ph)),\n", " Chart (H2, (x, y)),\n", " Chart (U, (x, y))]" ] }, "execution_count": 81, "metadata": {}, "output_type": "execute_result" } ], "source": [ "H2.atlas()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are actually 6 main charts, the other ones being subcharts:" ] }, { "cell_type": "code", "execution_count": 82, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[\\left(\\mathbb{H}^2,(X, Y)\\right), \\left(U,(r, {\\varphi})\\right), \\left(U,(R, {\\varphi})\\right), \\left(\\mathbb{H}^2,(u, v)\\right), \\left(U,({\\theta}, {\\varphi})\\right), \\left(\\mathbb{H}^2,(x, y)\\right)\\right]$ " ], "text/plain": [ "[Chart (H2, (X, Y)),\n", " Chart (U, (r, ph)),\n", " Chart (U, (R, ph)),\n", " Chart (H2, (u, v)),\n", " Chart (U, (th, ph)),\n", " Chart (H2, (x, y))]" ] }, "execution_count": 82, "metadata": {}, "output_type": "execute_result" } ], "source": [ "H2.top_charts()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The expression of the metric tensor in each of these charts is" ] }, { "cell_type": "code", "execution_count": 83, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = \\left( \\frac{Y^{2} + 1}{X^{2} + Y^{2} + 1} \\right) \\mathrm{d} X\\otimes \\mathrm{d} X + \\left( -\\frac{X Y}{X^{2} + Y^{2} + 1} \\right) \\mathrm{d} X\\otimes \\mathrm{d} Y + \\left( -\\frac{X Y}{X^{2} + Y^{2} + 1} \\right) \\mathrm{d} Y\\otimes \\mathrm{d} X + \\left( \\frac{X^{2} + 1}{X^{2} + Y^{2} + 1} \\right) \\mathrm{d} Y\\otimes \\mathrm{d} Y$ " ], "text/plain": [ "g = (Y^2 + 1)/(X^2 + Y^2 + 1) dX*dX - X*Y/(X^2 + Y^2 + 1) dX*dY - X*Y/(X^2 + Y^2 + 1) dY*dX + (X^2 + 1)/(X^2 + Y^2 + 1) dY*dY" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = \\left( \\frac{1}{r^{2} + 1} \\right) \\mathrm{d} r\\otimes \\mathrm{d} r + r^{2} \\mathrm{d} {\\varphi}\\otimes \\mathrm{d} {\\varphi}$ " ], "text/plain": [ "g = 1/(r^2 + 1) dr*dr + r^2 dph*dph" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = \\frac{4}{{\\left(R + 1\\right)}^{2} {\\left(R - 1\\right)}^{2}} \\mathrm{d} R\\otimes \\mathrm{d} R + \\frac{4 \\, R^{2}}{{\\left(R + 1\\right)}^{2} {\\left(R - 1\\right)}^{2}} \\mathrm{d} {\\varphi}\\otimes \\mathrm{d} {\\varphi}$ " ], "text/plain": [ "g = 4/((R + 1)^2*(R - 1)^2) dR*dR + 4*R^2/((R + 1)^2*(R - 1)^2) dph*dph" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = \\frac{4}{{\\left(u^{2} + v^{2} - 1\\right)}^{2}} \\mathrm{d} u\\otimes \\mathrm{d} u + \\frac{4}{{\\left(u^{2} + v^{2} - 1\\right)}^{2}} \\mathrm{d} v\\otimes \\mathrm{d} v$ " ], "text/plain": [ "g = 4/(u^2 + v^2 - 1)^2 du*du + 4/(u^2 + v^2 - 1)^2 dv*dv" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = \\frac{1}{\\cos\\left({\\theta}\\right)^{2}} \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\frac{\\sin\\left({\\theta}\\right)^{2}}{\\cos\\left({\\theta}\\right)^{2}} \\mathrm{d} {\\varphi}\\otimes \\mathrm{d} {\\varphi}$ " ], "text/plain": [ "g = cos(th)^(-2) dth*dth + sin(th)^2/cos(th)^2 dph*dph" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = \\frac{1}{y^{2}} \\mathrm{d} x\\otimes \\mathrm{d} x + \\frac{1}{y^{2}} \\mathrm{d} y\\otimes \\mathrm{d} y$ " ], "text/plain": [ "g = y^(-2) dx*dx + y^(-2) dy*dy" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for chart in H2.top_charts():\n", " show(g.display(chart.frame(), chart))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For each of these charts, the non-vanishing (and non-redundant w.r.t. the symmetry on the last 2 indices) **Christoffel symbols of $g$** are" ] }, { "cell_type": "code", "execution_count": 84, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\mathbb{H}^2,(X, Y)\\right)$ " ], "text/plain": [ "Chart (H2, (X, Y))" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{lcl} \\Gamma_{ \\phantom{\\, X} \\, X \\, X }^{ \\, X \\phantom{\\, X} \\phantom{\\, X} } & = & -\\frac{X Y^{2} + X}{X^{2} + Y^{2} + 1} \\\\ \\Gamma_{ \\phantom{\\, X} \\, X \\, Y }^{ \\, X \\phantom{\\, X} \\phantom{\\, Y} } & = & \\frac{X^{2} Y}{X^{2} + Y^{2} + 1} \\\\ \\Gamma_{ \\phantom{\\, X} \\, Y \\, Y }^{ \\, X \\phantom{\\, Y} \\phantom{\\, Y} } & = & -\\frac{X^{3} + X}{X^{2} + Y^{2} + 1} \\\\ \\Gamma_{ \\phantom{\\, Y} \\, X \\, X }^{ \\, Y \\phantom{\\, X} \\phantom{\\, X} } & = & -\\frac{Y^{3} + Y}{X^{2} + Y^{2} + 1} \\\\ \\Gamma_{ \\phantom{\\, Y} \\, X \\, Y }^{ \\, Y \\phantom{\\, X} \\phantom{\\, Y} } & = & \\frac{X Y^{2}}{X^{2} + Y^{2} + 1} \\\\ \\Gamma_{ \\phantom{\\, Y} \\, Y \\, Y }^{ \\, Y \\phantom{\\, Y} \\phantom{\\, Y} } & = & -\\frac{{\\left(X^{2} + 1\\right)} Y}{X^{2} + Y^{2} + 1} \\end{array}$ " ], "text/plain": [ "Gam^X_XX = -(X*Y^2 + X)/(X^2 + Y^2 + 1) \n", "Gam^X_XY = X^2*Y/(X^2 + Y^2 + 1) \n", "Gam^X_YY = -(X^3 + X)/(X^2 + Y^2 + 1) \n", "Gam^Y_XX = -(Y^3 + Y)/(X^2 + Y^2 + 1) \n", "Gam^Y_XY = X*Y^2/(X^2 + Y^2 + 1) \n", "Gam^Y_YY = -(X^2 + 1)*Y/(X^2 + Y^2 + 1) " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(U,(r, {\\varphi})\\right)$ " ], "text/plain": [ "Chart (U, (r, ph))" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{lcl} \\Gamma_{ \\phantom{\\, r} \\, r \\, r }^{ \\, r \\phantom{\\, r} \\phantom{\\, r} } & = & -\\frac{r}{r^{2} + 1} \\\\ \\Gamma_{ \\phantom{\\, r} \\, {\\varphi} \\, {\\varphi} }^{ \\, r \\phantom{\\, {\\varphi}} \\phantom{\\, {\\varphi}} } & = & -r^{3} - r \\\\ \\Gamma_{ \\phantom{\\, {\\varphi}} \\, r \\, {\\varphi} }^{ \\, {\\varphi} \\phantom{\\, r} \\phantom{\\, {\\varphi}} } & = & \\frac{1}{r} \\end{array}$ " ], "text/plain": [ "Gam^r_r,r = -r/(r^2 + 1) \n", "Gam^r_ph,ph = -r^3 - r \n", "Gam^ph_r,ph = 1/r " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(U,(R, {\\varphi})\\right)$ " ], "text/plain": [ "Chart (U, (R, ph))" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{lcl} \\Gamma_{ \\phantom{\\, R} \\, R \\, R }^{ \\, R \\phantom{\\, R} \\phantom{\\, R} } & = & -\\frac{2 \\, R}{R^{2} - 1} \\\\ \\Gamma_{ \\phantom{\\, R} \\, {\\varphi} \\, {\\varphi} }^{ \\, R \\phantom{\\, {\\varphi}} \\phantom{\\, {\\varphi}} } & = & \\frac{R^{3} + R}{R^{2} - 1} \\\\ \\Gamma_{ \\phantom{\\, {\\varphi}} \\, R \\, {\\varphi} }^{ \\, {\\varphi} \\phantom{\\, R} \\phantom{\\, {\\varphi}} } & = & -\\frac{R^{2} + 1}{R^{3} - R} \\end{array}$ " ], "text/plain": [ "Gam^R_R,R = -2*R/(R^2 - 1) \n", "Gam^R_ph,ph = (R^3 + R)/(R^2 - 1) \n", "Gam^ph_R,ph = -(R^2 + 1)/(R^3 - R) " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\mathbb{H}^2,(u, v)\\right)$ " ], "text/plain": [ "Chart (H2, (u, v))" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{lcl} \\Gamma_{ \\phantom{\\, u} \\, u \\, u }^{ \\, u \\phantom{\\, u} \\phantom{\\, u} } & = & -\\frac{2 \\, u}{u^{2} + v^{2} - 1} \\\\ \\Gamma_{ \\phantom{\\, u} \\, u \\, v }^{ \\, u \\phantom{\\, u} \\phantom{\\, v} } & = & -\\frac{2 \\, v}{u^{2} + v^{2} - 1} \\\\ \\Gamma_{ \\phantom{\\, u} \\, v \\, v }^{ \\, u \\phantom{\\, v} \\phantom{\\, v} } & = & \\frac{2 \\, u}{u^{2} + v^{2} - 1} \\\\ \\Gamma_{ \\phantom{\\, v} \\, u \\, u }^{ \\, v \\phantom{\\, u} \\phantom{\\, u} } & = & \\frac{2 \\, v}{u^{2} + v^{2} - 1} \\\\ \\Gamma_{ \\phantom{\\, v} \\, u \\, v }^{ \\, v \\phantom{\\, u} \\phantom{\\, v} } & = & -\\frac{2 \\, u}{u^{2} + v^{2} - 1} \\\\ \\Gamma_{ \\phantom{\\, v} \\, v \\, v }^{ \\, v \\phantom{\\, v} \\phantom{\\, v} } & = & -\\frac{2 \\, v}{u^{2} + v^{2} - 1} \\end{array}$ " ], "text/plain": [ "Gam^u_uu = -2*u/(u^2 + v^2 - 1) \n", "Gam^u_uv = -2*v/(u^2 + v^2 - 1) \n", "Gam^u_vv = 2*u/(u^2 + v^2 - 1) \n", "Gam^v_uu = 2*v/(u^2 + v^2 - 1) \n", "Gam^v_uv = -2*u/(u^2 + v^2 - 1) \n", "Gam^v_vv = -2*v/(u^2 + v^2 - 1) " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(U,({\\theta}, {\\varphi})\\right)$ " ], "text/plain": [ "Chart (U, (th, ph))" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{lcl} \\Gamma_{ \\phantom{\\, {\\theta}} \\, {\\theta} \\, {\\theta} }^{ \\, {\\theta} \\phantom{\\, {\\theta}} \\phantom{\\, {\\theta}} } & = & \\frac{\\sin\\left({\\theta}\\right)}{\\cos\\left({\\theta}\\right)} \\\\ \\Gamma_{ \\phantom{\\, {\\theta}} \\, {\\varphi} \\, {\\varphi} }^{ \\, {\\theta} \\phantom{\\, {\\varphi}} \\phantom{\\, {\\varphi}} } & = & -\\frac{\\sin\\left({\\theta}\\right)}{\\cos\\left({\\theta}\\right)} \\\\ \\Gamma_{ \\phantom{\\, {\\varphi}} \\, {\\theta} \\, {\\varphi} }^{ \\, {\\varphi} \\phantom{\\, {\\theta}} \\phantom{\\, {\\varphi}} } & = & \\frac{1}{\\cos\\left({\\theta}\\right) \\sin\\left({\\theta}\\right)} \\end{array}$ " ], "text/plain": [ "Gam^th_th,th = sin(th)/cos(th) \n", "Gam^th_ph,ph = -sin(th)/cos(th) \n", "Gam^ph_th,ph = 1/(cos(th)*sin(th)) " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\mathbb{H}^2,(x, y)\\right)$ " ], "text/plain": [ "Chart (H2, (x, y))" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{lcl} \\Gamma_{ \\phantom{\\, x} \\, x \\, y }^{ \\, x \\phantom{\\, x} \\phantom{\\, y} } & = & -\\frac{1}{y} \\\\ \\Gamma_{ \\phantom{\\, y} \\, x \\, x }^{ \\, y \\phantom{\\, x} \\phantom{\\, x} } & = & \\frac{1}{y} \\\\ \\Gamma_{ \\phantom{\\, y} \\, y \\, y }^{ \\, y \\phantom{\\, y} \\phantom{\\, y} } & = & -\\frac{1}{y} \\end{array}$ " ], "text/plain": [ "Gam^x_xy = -1/y \n", "Gam^y_xx = 1/y \n", "Gam^y_yy = -1/y " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for chart in H2.top_charts():\n", " show(chart)\n", " show(g.christoffel_symbols_display(chart=chart))" ] } ], "metadata": { "kernelspec": { "display_name": "SageMath 7.5", "language": "", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.13" } }, "nbformat": 4, "nbformat_minor": 0 }