Journal of Dynamical and Control Systems

, Volume 2, Issue 3, pp 359–421 | Cite as

Small sub-Riemannian balls onR3

  • El-H. Ch. El-Alaoui
  • J. -P. Gauthier
  • I. Kupka


This paper deals with sub-Riemannian metrics onR3 in the contact case. We study the singularities of the exponential mapping in the neighborhood of its pole. This is in stark contrast with the Riemannian case where this situation never occurs.

1991 Mathematics Subject Classification

53B 49L05 

Key words and phrases

Sub-Riemannian geometry contact structure differential invariant normal form conjugate locus 


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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • El-H. Ch. El-Alaoui
    • 1
  • J. -P. Gauthier
    • 2
  • I. Kupka
    • 3
  1. 1.INSA de Rouen, Department of MathematicsLMI, URA CNRS D 1378Mont Saint Aignan cedexFrance
  2. 2.Laboratoire de Mathématiques, AMS-LMI, URA CNRS 1378INSA de RouenMont-Saint-Aignan CedexFrance
  3. 3.Department of MathematicsUniversity of Paris VIParis cedes 05France

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