Symmetries of sub-Riemannian surfaces |
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Authors: | José Ricardo Arteaga B Mikhail Armenovich Malakhaltsev |
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Institution: | 1. Universidad de los Andes, Bogotá, Colombia;2. Kazan State University, Kazan, Russia |
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Abstract: | We obtain some results on symmetries of sub-Riemannian surfaces. In case of a contact sub-Riemannian surface we base on invariants found by Hughen 15]. 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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Keywords: | 58A17 53C05 53C17 58E25 |
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