# A.A. Agrachev, H. Chakir, J.-P. Gauthier, Sub-Riemannian metrics on $R^3$

Title: Sub-Riemannian metrics on R^3
Authors: A.A. Agrachev, H. Chakir, J.-P. Gauthier
Journal title: Proc. Canadian Math. Soc.
Year: 1998
Volume: 25
Pages: 29-78
Abstract:

This paper is a continuation of a series of papers of the authors dealing with sub-Riemannian metrics on $R^3$ in the contact case. Our purpose here in is twofold:
1. We prove the smoothness of a certain normal form, which is the analog of "normal coordinates" in Riemannian geometry. This normal form is crucial for the purpose of studying singularities of the exponential mapping. In our previous papers, it was a "formal" normal form only.
2. We finish with the generic classification for the singularities of the exponential mapping of a germ of a contact sub-Riemannian metric.