Flag Curvature of Invariant Randers Metrics on Homogeneous Manifolds

Abstract

In this article we review the recent results about the flag curvature of invariant Randers metrics on homogeneous manifolds and by using a counter example we show that the formula which obtained for the flag curvature of these metrics is incorrect. Then we give an explicit formula for the flag curvature of invariant Randers metrics on the naturally reductive homogeneous manifolds $(G/H,g)$, where the Randers metric induced by the invariant Riemannian metric $g$ and an invariant vector field $\tilde{X}$ which is parallel with $g$.

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• On the Randers metrics on two-step homogeneous nilmanifolds of dimension five
• The Relation Between Automorphism Group and Isometry Group of Randers Lie Groups
• Some Berwald Spaces of Non-positive flag Curvature
• Randers Metrics of Berwald type on 4-dimensional hypercomplex Lie groups
• On the left invariant Randers and Matsumoto metrics of Berwald type on 3-dimensional Lie groups
• Left Invariant Randers Metrics of Berwald type on Tangent Lie Groups
• Left invariant lifted $(\alpha ,\beta )$-metrics of Douglas type on tangent Lie groups