Image:UHS geodesics.png

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Geodesics in upper half space model of three-dimensional hyperbolic space H3. The metric is

ds^2 = \frac{dx^2+dy^2+dz^2}{x^2}, \; \; 0 < x < \infty, \; \; -infty < y,z < \infty

Some typical geodesics through one point are shown in black. They appear as semicircular arcs in the upper half space chart. The magenta plane represents the "sphere at infinity", which is located at x = 0 in this chart.

This is a png image converted by eog from a jpg image created by User:Hillman using Maple.


Hillman, the copyright holder of this work, has published or hereby publishes it under the following license:
GNU head Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation license, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation license".

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current13:08, 17 April 2007400×400 (2 KB)Melirius ({{ShouldBeSVG}} Geodesics in upper half space model of three-dimensional hyperbolic space '''H'''<sup>3</sup>. The metric is :<math> ds^2 = \frac{dx^2+dy^2+dz^2}{x^2}, \; \; 0 < x < \infty, \; \; -infty < y,z < \infty </math> Some typical geodesics throu)
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