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1 results

  • Sub-Riemannian Metrics: Minimalityof Abnormal Geodesics versus Subanalyticity

  • Andrei A. Agrachev, Andrei V. Sarychev
  • Journal:
    ESAIM: Control, Optimisation and Calculus of Variations / Volume 4 / 1999
    Published online by Cambridge University Press:
    15 August 2002, pp. 377-403
    Print publication:
    1999

  • We study sub-Riemannian (Carnot-Caratheodory) metrics defined bynoninvolutivedistributions on real-analytic Riemannian manifolds.We establish a connection between regularity properties of thesemetrics and the lack of length minimizing abnormal geodesics.Utilizing the results of the previous study of abnormal lengthminimizers accomplished by the authors in [Annales IHP. Analysenonlinéaire 13 , p. 635-690] we describe in thispaper two classes of the germs of distributions (called2-generating and medium fat) such that the correspondingsub-Riemannian metrics are subanalytic. To characterize theseclasses of distributions we determine the dimensions of themanifolds on which generic germs of distributions of given rankare respectively 2-generating or medium fat.