Curvature of sub-Riemannian spaces
Metric Geometry
2007-05-23 v1
Abstract
To any metric spaces there is an associated metric profile. The rectifiability of the metric profile gives a good notion of curvature of a sub-Riemannian space. We shall say that a curvature class is the rectifiability class of the metric profile. We classify then the curvatures by looking to homogeneous metric spaces. The classification problem is solved for contact 3 manifolds, where we rediscover a 3 dimensional family of homogeneous contact manifolds, with a distinguished 2 dimensional family of contact manifolds which don't have a natural group structure.
Cite
@article{arxiv.math/0311482,
title = {Curvature of sub-Riemannian spaces},
author = {Marius Buliga},
journal= {arXiv preprint arXiv:math/0311482},
year = {2007}
}