Measures of transverse paths in sub-Riemannian geometry

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 th...

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Bibliographic Details
Published in:Journal d'analyse mathématique (Jerusalem) 2003-12, Vol.91 (1), p.231-246
Main Authors: Falbel, Elisha, Jean, Frédéric
Format: Article
Language:English
Subjects:
Brownian motion
Riemann manifold
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Summary: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.[PUBLICATION ABSTRACT]
ISSN:0021-7670
1565-8538
DOI:10.1007/BF02788789