Randers Metrics of Isotropic S-Curvature
Randers Metrics of Isotropic S-Curvature
复制标题
DOI：
10.1007/978-3-642-24888-7_3
复制
发表时间：
2012
期刊：
影响因子：
--
通讯作者：
Xinyue Cheng;Z. Shen
中科院分区：
文献类型：
--
作者：
Xinyue Cheng;Z. Shen
在芬斯勒几何中有几个重要的几何量。Cartan挠率C是一个基本量。还有另一个量由Busemann-Hausdorff体积形式确定，即所谓的畸变τ。τ在每个切空间上的垂直微分产生平均Cartan挠率，C，τ和I是Finsler度量中刻画Riemann度量的基本非黎曼几何量，它们之间的关系为（1.17）和（1.18）.在这一章中，我们将引入一个新的量，它被定义为沿测地线沿着的畸变变化率。
There are several important geometric quantities in Finsler geometry. The Cartan torsionCis a primary quantity. There is another quantity which is determined by the Busemann-Hausdorff volume form, that is the so-called distortionτ. The vertical differential ofτon each tangent space gives rise to the mean Cartan torsion.C,τandIare the basic non-Riemannian geometric quantities which characterize Riemann metrics among Finsler metrics and are connected each other as (1.17) and (1.18). In this chapter, we are going to introduce a new quantity which is defined as a rate of change of the distortion along a geodesic.