{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Hyperbolic plane $\\mathbb{H}^2$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook illustrates some differential geometry capabilities of SageMath on the example of the hyperbolic plane. The corresponding tools have been developed within\n", "the [SageManifolds](http://sagemanifolds.obspm.fr) project (version 1.2, as included in SageMath 8.2).\n", "\n", "Click [here](https://raw.githubusercontent.com/sagemanifolds/SageManifolds/master/Worksheets/v1.2/SM_hyperbolic_plane.ipynb) to download the notebook file (ipynb format). To run it, you must start SageMath with the Jupyter notebook interface, 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": {}, "outputs": [ { "data": { "text/plain": [ "'SageMath version 8.2, Release Date: 2018-05-05'" ] }, "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": {}, "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": {}, "outputs": [], "source": [ "viewer3D = 'threejs' # must be 'threejs', jmol', 'tachyon' or None (default)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we tell Maxima, which is used by SageMath for simplifications of symbolic expressions, that all computations involve real variables:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\verb|real|$ " ], "text/plain": [ "'real'" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "maxima_calculus.eval(\"domain: real;\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We declare $\\mathbb{H}^2$ as a 2-dimensional differentiable manifold:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "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": 5, "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": 6, "metadata": {}, "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": 6, "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": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\mathbb{H}^2,(X, Y)\\right)$ " ], "text/plain": [ "Chart (H2, (X, Y))" ] }, "execution_count": 7, "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": 8, "metadata": {}, "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": 8, "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": 9, "metadata": {}, "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, online=True, 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": 10, "metadata": {}, "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": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(U,(r, {\\varphi})\\right)$ " ], "text/plain": [ "Chart (U, (r, ph))" ] }, "execution_count": 11, "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": 12, "metadata": {}, "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": 12, "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": 13, "metadata": {}, "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": 13, "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": 14, "metadata": {}, "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": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pol_to_hyp.display()" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "pol_to_hyp.set_inverse(sqrt(X^2+Y^2), atan2(Y, X)) " ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "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": 16, "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": 17, "metadata": {}, "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": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi1.restrict(U).display()" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "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, online=True, figsize=7)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "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": 19, "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", "$$ \\eta = \\mathrm{d}X\\otimes\\mathrm{d}X + \\mathrm{d}Y\\otimes\\mathrm{d}Y - \\mathrm{d}Z\\otimes\\mathrm{d}Z $$" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "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": 20, "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": 21, "metadata": {}, "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": 21, "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": 22, "metadata": {}, "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": 22, "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": 23, "metadata": {}, "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": 24, "metadata": {}, "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": 24, "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": 25, "metadata": {}, "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": 26, "metadata": {}, "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": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Ric.display(X_pol.frame(), X_pol)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "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": 28, "metadata": {}, "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": 28, "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": 29, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 29, "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": 30, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 30, "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": 31, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(U,(R, {\\varphi})\\right)$ " ], "text/plain": [ "Chart (U, (R, ph))" ] }, "execution_count": 31, "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": 32, "metadata": {}, "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": 32, "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": 33, "metadata": {}, "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": 33, "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": 34, "metadata": {}, "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": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pol_to_Pdisk.display()" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "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": 35, "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": 36, "metadata": {}, "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), \n", " aspect_ratio=1, viewer=viewer3D, online=True, figsize=7)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The expression of the metric tensor in terms of coordinates $(R,\\varphi)$:" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "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": 37, "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": 38, "metadata": {}, "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": 38, "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": 39, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\mathbb{H}^2,(u, v)\\right)$ " ], "text/plain": [ "Chart (H2, (u, v))" ] }, "execution_count": 39, "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": 40, "metadata": {}, "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": 40, "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": 41, "metadata": {}, "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": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Pdisk_to_Pdisk_cart.display()" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "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": 42, "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": 43, "metadata": {}, "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": 43, "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": 44, "metadata": { "scrolled": false }, "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, online=True, 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": 45, "metadata": {}, "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": 45, "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": 46, "metadata": {}, "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": 46, "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": 47, "metadata": {}, "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": 47, "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": 48, "metadata": {}, "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": 48, "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": 49, "metadata": {}, "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": 49, "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": 50, "metadata": {}, "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": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "hyp_to_Pdisk_cart.display()" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "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": 51, "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": 52, "metadata": {}, "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, online=True, figsize=7)" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 30 graphics primitives" ] }, "execution_count": 53, "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": 54, "metadata": {}, "outputs": [], "source": [ "H2.set_default_chart(X_Pdisk_cart)\n", "H2.set_default_frame(X_Pdisk_cart.frame())" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "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": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display(X_hyp.frame())" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "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": 56, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display()" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "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": 57, "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": 58, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(U,({\\theta}, {\\varphi})\\right)$ " ], "text/plain": [ "Chart (U, (th, ph))" ] }, "execution_count": 58, "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": 59, "metadata": {}, "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": 59, "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": 60, "metadata": {}, "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": 60, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Pdisk_to_spher.display()" ] }, { "cell_type": "code", "execution_count": 61, "metadata": {}, "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": 61, "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": 62, "metadata": {}, "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": 62, "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": 63, "metadata": {}, "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": 63, "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": 64, "metadata": {}, "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, \n", " color='orange', label_axes=False)\n", "show(graph_hyp + graph_Pdisk + graph_spher, aspect_ratio=1, viewer=viewer3D, online=True, \n", " 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": 65, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\mathbb{H}^2,(x, y)\\right)$ " ], "text/plain": [ "Chart (H2, (x, y))" ] }, "execution_count": 65, "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": 66, "metadata": {}, "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": 66, "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": 67, "metadata": {}, "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": 67, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher_to_hplane.display()" ] }, { "cell_type": "code", "execution_count": 68, "metadata": {}, "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": 68, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Pdisk_to_hplane = spher_to_hplane * Pdisk_to_spher\n", "Pdisk_to_hplane" ] }, { "cell_type": "code", "execution_count": 69, "metadata": {}, "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": 69, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Pdisk_to_hplane.display()" ] }, { "cell_type": "code", "execution_count": 70, "metadata": {}, "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": 70, "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": 71, "metadata": {}, "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": 71, "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": 72, "metadata": {}, "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": 72, "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": 73, "metadata": {}, "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": 73, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Pdisk_cart_to_hplane.display()" ] }, { "cell_type": "code", "execution_count": 74, "metadata": {}, "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": 74, "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": 75, "metadata": {}, "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": 75, "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": 76, "metadata": {}, "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)}, \n", " number_values=15, color='brown', label_axes=False)\n", "show(graph_hyp + graph_Pdisk + graph_spher + graph_hplane, aspect_ratio=1, viewer=viewer3D,\n", " online=True, 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": 77, "metadata": {}, "outputs": [], "source": [ "pol_to_hplane = Pdisk_to_hplane * pol_to_Pdisk" ] }, { "cell_type": "code", "execution_count": 78, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "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, \n", " 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": 79, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 64 graphics primitives" ] }, "execution_count": 79, "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": 80, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "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": 81, "metadata": {}, "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": 81, "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": 82, "metadata": {}, "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": 82, "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": 83, "metadata": {}, "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": 83, "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": 84, "metadata": {}, "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": 85, "metadata": {}, "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 8.2", "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": "2.7.14" } }, "nbformat": 4, "nbformat_minor": 1 }