{ "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](https://sagemanifolds.obspm.fr) project (version 1.3, as included in SageMath 8.3).\n", "\n", "Click [here](https://raw.githubusercontent.com/sagemanifolds/SageManifolds/master/Worksheets/v1.3/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 8.3, Release Date: 2018-08-03'" ] }, "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 8.3", "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": "2.7.15" } }, "nbformat": 4, "nbformat_minor": 1 }