Local Equivalence Problem for Sub-Riemannian Structures
Differential Geometry
2011-07-21 v1
Abstract
We solve the local equivalence problem for sub-Riemannian structures on (2n + 1)-dimensional manifolds. We show that two sub-Riemannian structures are locally equivalent if and only if? their corresponding canonical linear connections are equivalent. When n = 1, these connections coincide with the generalized Tanaka-Webster connection of the corresponding contact metric structure. We show that in dimension > 5, there may not be any contact metric manifolds associated with a given sub-Riemannian structure.
Cite
@article{arxiv.1107.3847,
title = {Local Equivalence Problem for Sub-Riemannian Structures},
author = {Vladimir Krouglov},
journal= {arXiv preprint arXiv:1107.3847},
year = {2011}
}
Comments
11 pages, all comments are wellcome