The flag curvature of invariant (alpha, beta)-metrics of type (alpha+beta)(2)/alpha

摘要

In this paper, we study the flag curvature of invariant (alpha, beta)-metrics of the form (alpha+beta)(2)/alpha on homogeneous spaces and Lie groups. We give a formula for the flag curvature of invariant metrics of the form F = (alpha+beta)(2)/alpha a such that alpha 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.