The minimal number of homogeneous geodesics depending on the signature of the Killing form

2021/04/13 by Dusek, Zdenek
#53C22 #53C30 #53C60 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2104.06082

Abstract

The existence of at least two homogeneous geodesics in any homogeneous Finsler manifold was proved in a previous paper by the author. The examples of solvable Lie groups with invariant Finsler metric which admit just two homogeneous geodesics were presented in another paper. In the present work, it is shown that a homogeneous Finsler manifold with indefinite Killing form admits at least four homogeneous geodesics. Examples of invariant Randers metrics on Lie groups with definite Killing form admitting just two homogeneous geodesics and examples with indefinite Killing form admitting just four homogeneous geodesics are presented.

Related

• Homogeneous geodesics of left invariant Finsler metrics
• Two-step homogeneous geodesics in some homogeneous Finsler manifolds
• The metric geometry of infinite dimensional Lie groups and their\n homogeneous spaces
• Metric operator and geodesic orbit property for a standard homogeneous Finsler metric
• Very standard homogeneous Finsler manifolds with positive flag curvature