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arXiv · 0906.5041

Symmetries of sub-Riemannian surfaces

Mikhail Armenovich Malakhaltsev·José Ricardo Arteaga
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Abstract

We obtain some results on symmetries of sub-Riemannian surfaces. In case of contact sub-Riemannian surface we base on invariants found by Hughen \cite{Hughen}. Using these invariants, we find conditions under which a sub-Riemannian surface does not admit symmetries. If a surface admits symmetries, we show how invariants help to find them. It is worth noting, that the obtained conditions can be explicitly checked for a given contact sub-Riemannian surface. Also, we consider sub-Riemannian surfaces which are not contact and find their invariants along the surface where the distribution fails to be contact.

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Mikhail Armenovich Malakhaltsev, José Ricardo Arteaga. 2009-08-26. Symmetries of sub-Riemannian surfaces. https://arxiv.org/abs/0906.5041

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