Invariant Finsler metrics on homogeneous manifolds

Abstract

In this paper, we study invariant Finsler metrics on homogeneous manifolds. We first give an algebraic description of these metrics and obtain a necessary and sufficient condition for a homogeneous manifold to have invariant Finsler metrics. As a special case, we study bi-invariant Finsler metrics on Lie groups and obtain a necessary and sufficient condition for a Lie group to have bi-invariant Finsler metrics. Finally, we provide some conditions for a homogeneous manifold to admit invariant non-Riemannian Finsler metrics and present some interesting examples.