Homogeneous geodesics in homogeneous Finsler spaces
Homogeneous geodesics in homogeneous Finsler spaces
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DOI：
10.1016/j.geomphys.2006.11.004
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发表时间：
2007-04
影响因子：
1.5
通讯作者：
D. Latifi
中科院分区：
文献类型：
--
作者：
D. Latifi
本文研究了齐性Finsler空间中的齐性测地线。我们首先给出一个简单的标准，特点测地线向量。我们证明了李群上相对于双不变Finsler度量的测地线是单参数子群的陪集。证明了紧致半单李群上存在无穷多条齐次测地线。我们引入了自然约化齐性Finsler空间的概念。作为特例，我们研究了齐性兰德斯空间中的齐性测地线。最后，我们研究了齐次测地线的曲率性质。特别地，我们证明了S-曲率沿着齐次测地线为零。
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.