Symmetries of sub-Riemannian surfaces

Details Symmetries of sub-Riemannian surfaces Symmetries of sub-Riemannian surfaces

2009-06-27

arxiv.org/abs/0906.5041v2

Mathematics

Differential Geometry

Scientific paper

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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