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

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)].


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


Zbl 0954.53001
Full Text: DOI