The geodesic graph of Riemannian spaces all geodesics of which are orbits of 1-parameter isometry groups is constructed by J. Szenthe in 1976 and it became a basic tool for studying such spaces, called g.o. spaces. This infinitesimal structure corresponds to the reductive complement m in the case of naturally reductive spaces. The systematic study of Riemannian g.o. spaces is started by O. Kowa...

The work proposes a general background of the theory of field interactions and strings in spaces with higher order anisotropy. Our approach proceeds by developing the concept of higher order anisotropic superspace which unifies the logical and mathematical aspects of modern Kaluza– Klein theories and generalized Lagrange and Finsler geometry and leads to modelling of physical processes on highe...

David Hilbert discovered in 1895 an important metric that is canonically associated to an arbitrary convex domain Ω in the Euclidean (or projective) space. This metric is known to be Finslerian, and the usual proof of this fact assumes a certain degree of smoothness of the boundary of Ω, and refers to a theorem by Busemann and Mayer that produces the norm of a tangent vector from the distance f...

In this article, we review the current status of Finsler–Lagrange geometry and generalizations. The goal is to aid non–experts on Finsler spaces, but physicists and geometers skilled in general relativity and particle theories, to understand the crucial importance of such geometric methods for applications in modern physics. We also would like to orient mathematicians working in generalized Fin...

The aim of the present paper is to provide a global presentation, as complete as we can, of the theory of special Finsler manifolds. We introduce and investigate globally (or intrinsically, free from local coordinates) many of the most important and commonly used special Finsler manifolds : locally Minkowskian, Berwald, Landesberg, general Landesberg, P -reducible, C-reducible, semi-C-reducible...

It is reasonably well-known that birefringent crystal optics can to some extent be described by the use of pseudo–Finslerian spacetimes (an extension of the natural pseudo-Riemannian Minkowski spacetime one encounters in mono-refringent situations). What is less commonly appreciated is that there are two separate and quite disjoint pseudo–Finsler structures for the two photon polarizations, and...

In this paper, we study a class of Finsler metrics with orthogonal invariance. We find an equation that characterizes these Finsler metrics of almost vanishing H-curvature. As a consequence, we show that all orthogonally invariant Finsler metrics of almost vanishing H-curvature are of almost vanishing Ξ-curvature and corresponding one forms are exact, generalizing a result previously only known...

The notion of holomorphic bisectional curvature for a complex Finsler space (M, F ) is defined with respect to the Chern complex linear connection on the pull-back tangent bundle. By means of holomorphic curvature and holomorphic flag curvature of a complex Finsler space, a special approach is emloyed to obtain the characterizations of the holomorphic bisectional curvature. For the class of gen...

In this paper we consider a dominating Finsler metric on a complete Riemannian manifold. First we prove that the energy integral of the Finsler metric satisfies the Palais-Smale condition, and ask for the number of geodesics with endpoints in two given submanifolds. Using Lusternik-Schnirelman theory of critical points we obtain some multiplicity results for the number of Finsler-geodesics betw...