in this paper, we study a class of finsler metrics which contains the class of p-reducible andgeneral relatively isotropic landsberg metrics, as special cases. we prove that on a compact finsler manifold,this class of metrics is nothing other than randers metrics. finally, we study this class of finsler metrics withscalar flag curvature and find a condition under which these metrics reduce to r...

In the present paper we submit for study a new class of Finsler spaces. Through restricting the homogeneity condition from the definition of a complex Finsler metric to real scalars, λ ∈ R, is obtained a wider class of complex spaces, called by us the R−complex Finsler spaces. Two subclasses are taken in consideration: the Hermitian and the non-Hermitian R−complex Finsler spaces. In an R−comple...

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 Finsler and Kähler g...

It is the Hilbert’s Fourth Problem to characterize the (not-necessarilyreversible) distance functions on a bounded convex domain in R such that straight lines are shortest paths. Distance functions induced by a Finsler metric are regarded as smooth ones. Finsler metrics with straight geodesics said to be projective. It is known that the flag curvature of any projective Finsler metric is a scala...

In Finsler geometry, there are infinitely many models of constant curvature. The Funk metrics, the Hilbert-Klein metrics and the Bryant metrics are projectively flat with non-zero constant curvature. A recent example constructed by the author is projectively flat with zero curvature. In this paper, we introduce a technique to construct non-projectively flat Finsler metrics with zero curvature i...

Smooth Finsler metrics are a natural generalization of Riemannian ones and have been widely studied in the framework of differential geometry. The definition can be weakened by allowing the metric to be only Borel measurable. This generalization is necessary in view of applications, such as, for instance, optimization problems. In this paper we show that smooth Finsler metrics are dense in Bore...

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...

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...