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Siberian Mathematical Journal

, Volume 47, Issue 2, pp 209–238 | Cite as

Metrics and tangent cones of uniformly regular Carnot—Carathéodory spaces

  • A. V. Greshnov
Article

Abstract

Given a uniformly regular Carnot—Carathéodory space, we prove equivalence of the quasimetrics generated by various bases of vector fields which agree with filtration of the space. We prove a theorem on a nilpotent tangent cone for a uniformly regular Carnot—Carathéodory space furnished with quasimetrics. As a consequence, we obtain a theorem on isomorphism of nilpotent tangent cones defined at a common distinguished point.

Keywords

Carnot—Carathéodory space nilpotent group 

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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • A. V. Greshnov
    • 1
  1. 1.Sobolev Institute of MathematicsNovosibirskRussia

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