The flag curvature of invariant (α, β)-metrics of type (α+β)2/α

Abstract

In this paper, we study the flag curvature of invariant (α, β)-metrics of the form on homogeneous spaces and Lie groups. We give a formula for the flag curvature of invariant metrics of the form such that α is induced by an invariant Riemannian metric g on the homogeneous space and the Chern connection of F coincides to the Levi-Civita connection of g. Then some conclusions in the cases of naturally reductive homogeneous spaces and Lie groups are given. © 2008 IOP Publishing Ltd.