Homogeneous geodesics of left invariant Finsler metrics

Details Homogeneous geodesics of left invariant Finsler metrics Homogeneous geodesics of left invariant Finsler metrics

2007-11-28

arxiv.org/abs/0711.4480v1

Mathematics

Differential Geometry

Scientific paper

In this paper, we study the set of homogeneous geodesics of a leftinvariant Finsler metric on Lie groups. We first give a simple criterion that characterizes geodesic vectors. As an application, we study some geometric properties of bi-invariant Finsler metrics on Lie groups. In particular a necessary and sufficient condition that left-invariant Randers metrics are of Berwald type is given. Finally a correspondence of homogeneous geodesics to critical points of restricted Finsler metrics is given. Then results concerning the existence homogeneous geodesics are obtained.

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