Measures of Transverse Paths in Sub-Riemannian Geometry

Elisha Falbel and Frédéric Jean
december, 2003
Publication type:
Paper in peer-reviewed journals
Journal d'Analyse Mathematique, vol. 91(1), pp. 231-246
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.
    author={Elisha Falbel and Frédéric Jean },
    title={Measures of Transverse Paths in Sub-Riemannian Geometry },
    doi={10.1007/BF02788789 },
    journal={Journal d'Analyse Mathematique },
    year={2003 },
    volume={91(1) },