Flag curvature of invariant Randers metrics on homogeneous manifolds

Abstract

In this paper we review the recent results about the flag curvature of invariant Randers metrics on homogeneous manifolds. By using some counterexamples we show that the formula 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 naturally reductive homogeneous manifolds (G/H, g), where the Randers metric is induced by the invariant Riemannian metric g and an invariant vector field which is parallel with g. © 2006 IOP Publishing Ltd.