{ "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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", "