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

Anna Korolko

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arXiv · 1010.4392

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

Anna Korolko

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Abstract

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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Anna Korolko. 2010-10-21. Sub-semi-Riemannian geometry on $H$-type groups. https://arxiv.org/abs/1010.4392

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