Invariant Randers metrics on homogeneous Riemannian manifolds. (English) Zbl 1049.83005

Deng, Shaoqiang; Hou, Zixin

J. Phys. A, Math. Gen. 37, No. 15, 4353-4360 (2004); corrigendum ibid. 39, 5249-5250 (2006).

Summary: This paper studies Randers metrics on homogeneous Riemannian manifolds. It turns out that we can give a complete description of the invariant Randers metrics on a homogeneous Riemannian manifold as well as the geodesics, the flag curvatures. This result provides a convenient method to construct globally defined Berwald space which is neither Riemannian nor locally Minkowskian and gives another explanation of the example of D. Bao, S.-S. Chern and Z. Shen [An introduction to Riemannian-Finsler geometry (Berlin: Springer) (1999; Zbl 0954.53001)].

MSC:

83C10	Equations of motion in general relativity and gravitational theory
53C60	Global differential geometry of Finsler spaces and generalizations (areal metrics)
53C30	Differential geometry of homogeneous manifolds
83D05	Relativistic gravitational theories other than Einstein’s, including asymmetric field theories

Keywords:

Randers metrics; homogeneous Riemannian manifolds; geodesics

Citations:

Zbl 0954.53001