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

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

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 ${\displaystyle x=0}$ in this chart.

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

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