Homogeneous geodesics in homogeneous Finsler spaces |
| |
Authors: | Dariush Latifi |
| |
Affiliation: | Faculty of Mathematics and Computer Science, Amirkabir University of Technology, 424 Hafez Ave., 15914 Tehran, Iran |
| |
Abstract: | In this paper, we study homogeneous geodesics in homogeneous Finsler spaces. We first give a simple criterion that characterizes geodesic vectors. We show that the geodesics on a Lie group, relative to a bi-invariant Finsler metric, are the cosets of the one-parameter subgroups. The existence of infinitely many homogeneous geodesics on the compact semi-simple Lie group is established. We introduce the notion of a naturally reductive homogeneous Finsler space. As a special case, we study homogeneous geodesics in homogeneous Randers spaces. Finally, we study some curvature properties of homogeneous geodesics. In particular, we prove that the S-curvature vanishes along the homogeneous geodesics. |
| |
Keywords: | 53C60 53C35 53C30 53C22 |
本文献已被 ScienceDirect 等数据库收录! |
|