Homogeneous geodesics in homogeneous Finsler spaces

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 compact semi-simple Lie group is established. We introduce the notion of 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.

References in corpus (1)

• Lorentzian homogeneous spaces admitting a homogeneous structure of type T1+T3

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• Homogeneous geodesics of left invariant Finsler metrics
• On globally Symmetric Finsler spaces
• Geometry of left invariant Randers metric on the Heisenberg group
• On the flag curvature of a homogeneous Finsler sapce with generalized $m$-Kropina metric
• Geodesic orbit metrics on homogeneous spaces constructed by strongly isotropy irreducible spaces
• Two-step homogeneous geodesics in some homogeneous Finsler manifolds