In this paper we introduce the class of R-complex Finsler spaces with (α, β)-metrics and study some important exemples: R-complex Randers spaces, R-complex Kropina spaces. The metric tensor field of a R-complex Finsler space with (α, β)-metric is determined (§2). A special approach is dedicated to the R-complex Randers spaces (§3). AMS Mathematics Subject Classification (2000): 53B40, 53C60

Based on the analogue spacetime programme, and many other ideas currently mooted in “quantum gravity”, there is considerable ongoing speculation that the usual pseudoRiemannian (Lorentzian) manifolds of general relativity might eventually be modified at short distances. Two specific modifications that are often advocated are the adoption of Finsler geometries (or more specifically, pseudo-Finsl...

Equality of hh -curvatures of the Berwald and Cartan connections leads to a new class of Finsler metrics, socalled BC-generalized Landsberg metrics. Here, we prove that every BC-generalized Landsberg metric of scalar flag curvature with dimension greater than two is of constant flag curvature.

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 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