Measures of transverse paths in sub-Riemannian geometry

被引：13
|
作者：
Falbel, E
Jean, F
机构：
[1] Univ Paris 06, Math Inst, F-75013 Paris, France
[2] Ecole Natl Super Tech Avancees, Lab Math Appl, F-75739 Paris, France
来源：
JOURNAL D ANALYSE MATHEMATIQUE | 2003年 / 91卷 / 1期
关键词：
D O I：
10.1007/BF02788789
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
引用
收藏
页码：231 / 246
页数：16
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