Measures of Transverse Paths in Sub-Riemannian Geometry - Archive ouverte HAL Access content directly
Journal Articles Journal d'analyse mathématique Year : 2003

Measures of Transverse Paths in Sub-Riemannian Geometry

Elisha Falbel
  • Function : Author
Frédéric Jean

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.

Dates and versions

hal-00989831 , version 1 (12-05-2014)

Identifiers

Cite

Elisha Falbel, Frédéric Jean. Measures of Transverse Paths in Sub-Riemannian Geometry. Journal d'analyse mathématique, 2003, 91 (1), pp.231-246. ⟨10.1007/BF02788789⟩. ⟨hal-00989831⟩

Collections

ENSTA UMA_ENSTA
55 View
0 Download

Altmetric

Share

Gmail Facebook X LinkedIn More