On sub-Riemannian manifolds, any neighborhood os any point contains geodesics, whic are not length minimizires; the closures of the cut and the conjugate loci of a point contrain . We study this phenomenon in the case of a contact underlying distribution, essentially in the lowest possible dimension 3, where we extract differential invariants related to the singularities of the cut and the conjugate loci near and give a generic classification of these singularities.
Title: Exponential mappings for contact sub-Riemannian structures
Authors: A.A. Agrachev
Journal title: Dynamical and Control Systems