Symmetries of sub-Riemannian surfaces
Differential Geometry
2009-08-27 v2 Dynamical Systems
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.
Cite
@article{arxiv.0906.5041,
title = {Symmetries of sub-Riemannian surfaces},
author = {Mikhail Armenovich Malakhaltsev and José Ricardo Arteaga},
journal= {arXiv preprint arXiv:0906.5041},
year = {2009}
}