English

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.

Keywords

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

R2 v1 2026-06-21T18:39:08.225Z