Journal d’Analyse Mathématique

, Volume 91, Issue 1, pp 231–246 | Cite as

Measures of transverse paths in sub-Riemannian geometry

  • Elisha Falbel
  • Frédéric Jean
Article

Abstract

We define a class of lengths of paths in a sub-Riemannian manifold. It includes the length of horizontal paths but also measures the length of transverse paths. It is obtained by integrating an infinitesimal measure which generalizes the norm on the tangent space. This requires the definition and the study of the metric tangent space (in Gromov's sense). As an example, we compute those measures in the case of contact sub-Riemannian manifolds.

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Copyright information

© The Hebrew University Magnes Press 2003

Authors and Affiliations

  • Elisha Falbel
    • 1
  • Frédéric Jean
    • 2
  1. 1.Institut de MathématiquesUniversité Paris 6ParisFrance
  2. 2.Laboratoire de Mathématiques Appliquéesécole Nationale Supérieure des Techniques AvancéesParisFrance

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