А.А. Аграчëв, У любой субримановой метрики есть точки гладкости

Title: Any sub-Riemannian metric has points of smoothness
Authors: A.A. Agrachev
Journal title: Russian Math. Dokl.
Year: 2009
Issue: 1
Volume: 79
Pages: 1-3

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.