Sub-semi-Riemannian geometry on $H$-type groups

Details Sub-semi-Riemannian geometry on $H$-type groups Sub-semi-Riemannian geometry on $H$-type groups

2010-10-21

arxiv.org/abs/1010.4392v1

Mathematics

Differential Geometry

Scientific paper

We consider $H$(eisenberg)-type groups whose law of left translation gives rise to a bracket generating distribution of step 2. In the contrast with sub-Riemannian studies we furnish the horizontal distribution with a nondegenerate indefinite metric of arbitrary index and investigate the problem concerning causal geodesics on underlying manifolds. The exact formulae for geodesics are obtained.

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