WOLFRAM|DEMONSTRATIONS PROJECT

Torus in Nil-Space

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large radius
small radius
b-translation
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
P
3
S

4
V
,
V
4
,
). Here, the tori of the Nil-space are visualized.