Journal of Dynamical and Control Systems

, Volume 2, Issue 3, pp 321–358 | Cite as

Exponential mappings for contact sub-Riemannian structures

  • A. A. Agrachev


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.

1991 Mathematics Subject Classification

53B 49L05 

Key words and phrases

Sub-Riemannian geometry contact structure differential invariants conjugate locus dut locus 


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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • A. A. Agrachev
    • 1
  1. 1.Steklov Mathematical InstituteMoscowRussia

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