WOLFRAM|DEMONSTRATIONS PROJECT

Geodesic Cone in Nil-Geometry

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θ
0.3
α
0
W. Heisenberg's real matrix group provides a noncommutative translation group of an affine three-space. The Nil-geometry, which is one of the eight Thurston three-geometries, can be derived from this group. E. Molnár proved that the homogeneous three-spaces have a unified interpretation in the projective three-sphere
3
PS

4
V
,
V
4
,
). In this Demonstration a geodesic line rotated around the
z
axis, (a "geodesic cone") is visualized.