Any sub-Riemannian Metric has Points of Smoothness
Differential Geometry
2008-09-25 v2 Optimization and Control
Abstract
We prove the result stated in the title; it is equivalent to the existence of a regular point of the sub-Riemannian exponential mapping. We also prove that the metric is analytic on an open everywhere dense subset in the case of a complete real-analytic sub-Riemannian manifold.
Cite
@article{arxiv.0808.4059,
title = {Any sub-Riemannian Metric has Points of Smoothness},
author = {Andrei Agrachev},
journal= {arXiv preprint arXiv:0808.4059},
year = {2008}
}