Measures of transverse paths in sub-Riemannian geometry
Measures of transverse paths in sub-Riemannian geometry
复制标题
亚黎曼几何中横向路径的测量
DOI：
10.1007/bf02788789
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发表时间：
2003
期刊：
影响因子：
--
通讯作者：
F. Jean
中科院分区：
文献类型：
--
作者：
E. Falbel;F. Jean
定义了一类次黎曼流形中的路长。它包括水平路径的长度，但也测量横向路径的长度。它是通过积分一个无穷小测度而得到的，该测度推广了切空间上的范数。这需要定义和研究度量切空间（在格罗莫夫的意义上）。作为一个例子，我们计算这些措施的情况下，接触子黎曼流形。
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.