Homogeneous geodesics in homogeneous Finsler spaces

By D. Latifi. 2007

100 citations recorded by the source corpus.

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.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/b295c51f24b9fcd6420497dff35756474fbc45ed

Citations in the corpus