The notion of holomorphic bi-flag 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 devoted to obtain the characterizations of the holomorphic bi-flag curvature. For the class of generalized...

In this work we study an anisotropic model of general relativity based on the framework of Finsler geometry. The observed anisotropy of the microwave background radiation [8] is incorporated in the Finslerian structure of space-time. We also examine the electromagnetic (e.m.) field equations in our space. As a result a modified wave equation of e.m. waves yields.

using the electrostatic capacity of a condenser, the existence of a distance function on a finsler space is discussed. this distance function divides finsler spaces into the two classes, denoted here by i and ii. the topology generated by this distance on the finsler spaces of class ii coincides with its intrinsic topology. this work provides a natural extension of mathematical analysis tools n...

We elaborate an unified geometric approach to classical mechanics, Riemann–Finsler spaces and gravity theories on Lie algebroids provided with nonlinear connection (N–connection) structure. There are investigated the conditions when the fundamental geometric objects like the anchor, metric and linear connection, almost sympletic and related almost complex structures may be canonically defined b...

We formulate an approach to the geometry of Riemann–Cartan spaces provided with nonholonomic distributions defined by generic off-diagonal and nonsymmetric metrics inducing effective nonlinear and affine connections. Such geometries can be modelled by moving nonholonomic frames on (pseudo) Riemannian manifolds and describe various types of nonholonomic Einstein, Eisenhart–Moffat and Finsler–Lag...

In this paper we parallelly build up the theories of normed linear spaces and of linear spaces with indefinite metric, called also Minkowski spaces for finite dimensions in the literature. In the first part of this paper we collect the common properties of the semi-and indefinite-inner-products and define the semi-indefinite-inner-product and the corresponding structure, the semi-indefinite-inn...

In this paper we first study some global properties of the energy functional on a nonreversible Finsler manifold. In particular we present a fully detailed proof of the Palais–Smale condition under the completeness of the Finsler metric. Moreover we define a Finsler metric of Randers type, which we call Fermat metric, associated to a conformally standard stationary spacetime. We shall study the...

We prove that any simply connected and complete Riemannian manifold, on which a Randers metric of positive constant flag curvature exists, must be diffeomorphic to an odd-dimensional sphere, provided a certain 1-form vanishes on it. 1. Introduction. The geometry of Finsler manifolds of constant flag curvature is one of the fundamental subjects in Finsler geometry. Akbar-Zadeh [1] proved that, u...

Some physicists suggest that to more adequately describe the causal structure of space-time, it is necessary to go beyond the usual pseudoRiemannian causality, to a more general Finsler causality. In this general case, the set of all the events which can be influenced by a given event is, locally, a generic convex cone, and not necessarily a pseudoReimannian-style quadratic cone. Since all curr...