Let M = G/K be a generalized flag manifold, that is the adjoint orbit of a compact semisimple Lie group G. We use the variational approach to find invariant Einstein metrics for all flag manifolds with two isotropy summands. We also determine the nature of these Einstein metrics as critical points of the scalar curvature functional under fixed volume. 2000 Mathematics Subject Classification. Pr...

For non-reversible Finsler metrics of positive flag curvature on spheres and projective spaces we present results about the number and the length of closed geodesics and about their stability properties. 2000 MSC classification: 53C22; 53C60; 58E10

For non-reversible Finsler metrics of positive flag curvature on spheres and projective spaces we present results about the number and the length of closed geodesics and about their stability properties.

In this paper we study spherically symmetric metrics on a space in $\mathbb{R}^n$ with scalar and constant flag curvature also obtain families of type metrics. Many explicit examples are provided for Douglas curvature. Furthermore, new projectively flat Finsler given. We provide family which not type.