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.

We develop the method of anholonomic frames with associated nonlinear connec-tion (in brief, N–connection) structure and show explicitly how geometries with lo-cal anisotropy (various type of Finsler–Lagrange–Cartan–Hamilton geometry) can bemodeled in the metric–affine spaces. There are formulated the criteria when such gen-eralized Finsler metrics are effectively induced in the...

In this essay, we study the sufficient and necessary conditions for a Randers metrc to be of constant Ricci curvature, without the restriction of strong convexity (regularity). A classification result for the case ‖β‖α > 1 is provided, which is similar to the famous Bao-Robles-Shen’s result for strongly convex Randers metrics (‖β‖α < 1). Based on some famous vacuum Einstein metrics in General R...

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