Invariant Finsler metrics on homogeneous manifolds. (English) Zbl 1062.58007

Deng, Shaoqiang; Hou, Zixin

J. Phys. A, Math. Gen. 37, No. 34, 8245-8253 (2004).

Summary: 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.

MSC:

58B20

Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds