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.
Any sub-Riemannian metric has points of smoothness / Agrachev, A.. - In: DOKLADY MATHEMATICS. - ISSN 1064-5624. - 79:1(2009), pp. 45-47. [10.1134/S106456240901013X]
Any sub-Riemannian metric has points of smoothness
Agrachev, A.
2009-01-01
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.File in questo prodotto:
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