A Natural Connection on (2,3) Sub-Riemannian Manifolds
Differential Geometry
2009-05-16 v2
Abstract
We build an analogue for the Levi-Civita connection on Riemannian manifolds for sub-Riemannian manfiolds modeled on the Heisenberg group. We demonstrate some geometric properties of this connection to justify our choice and show that this connection is unique in having these properties.
Cite
@article{arxiv.0810.4141,
title = {A Natural Connection on (2,3) Sub-Riemannian Manifolds},
author = {Daniel R. Cole},
journal= {arXiv preprint arXiv:0810.4141},
year = {2009}
}
Comments
14 pages, no figures. Fixed a small error in the main theorem