Abstract
On sub-Riemannian manifolds any neighborhood of any point contains geodesics which are not length minimizers; the closures of the cut and the conjugate loci of any pointq containq. We study this phenomenon in the case of a contact distribution, essentially in the lowest possible dimension 3, where we extract differential invariants related to the singularities of the cut and the conjugate loci nearq and give a generic classification of these singularities.
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Partially supported by the Russian Foundation for Fundamental Research, grant 95-01-00310 and by INTAS project 93-893.
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Agrachev, A.A. Exponential mappings for contact sub-Riemannian structures. Journal of Dynamical and Control Systems 2, 321–358 (1996). https://doi.org/10.1007/BF02269423
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DOI: https://doi.org/10.1007/BF02269423