On the flag curvature of invariant Randers metrics

Abstract

In the present paper, the flag curvature of invariant Randers metrics on homogeneous spaces and Lie groups is studied. We first give an explicit formula for the flag curvature of invariant Randers metrics arising from invariant Riemannian metrics on homogeneous spaces and, in special case, Lie groups. We then study Randers metrics of constant positive flag curvature and complete underlying Riemannian metric on Lie groups. Finally we give some properties of those Lie groups which admit a left invariant non-Riemannian Randers metric of Berwald type arising from a left invariant Riemannian metric and a left invariant vector field.

References in corpus (2)

• Flag Curvature of Invariant Randers Metrics on Homogeneous Manifolds
• Induced Invariant Finsler Metrics on Quotient Groups

Cited by in corpus (6)

• The Relation Between Automorphism Group and Isometry Group of Randers Lie Groups
• On the Randers metrics on two-step homogeneous nilmanifolds of dimension five
• Some Berwald Spaces of Non-positive flag Curvature
• Randers Metrics of Berwald type on 4-dimensional hypercomplex Lie groups
• On the curvature of invariant Kropina metrics
• On the flag curvature of a homogeneous Finsler sapce with generalized $m$-Kropina metric