in this paper the general relatively isotropic l -curvature finsler metrics are studied. it isshown that on constant relatively landsberg spaces, the concepts of weakly landsbergian, landsbergianand generalized landsbergian metrics are equivalent. some necessary conditions for a relativelyisotropic l -curvature finsler metric to be a riemannian metric are also found.

In this paper we continue the study of the complex Beil metrics, in complex Finsler geometry, [18]. Primarily, we determine the main geometric objects corresponding to these metrics, e.g. the Chern-Finsler complex non-linear connection, the Chern-Finsler complex linear connection and the holomorphic curvature. We focus our study on the cases when a complex Finsler space, endowed with a complex ...

We discuss general notions of metrics and of Finsler structures which we call weak metrics and weak Finsler structures. Any convex domain carries a canonical weak Finsler structure, which we call its tautological weak Finsler structure. We compute distances in the tautological weak Finsler structure of a domain and we show that these are given by the so-called Funk weak metric. We conclude the ...

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...

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This paper is devoted to a study of geodesics of Finsler metrics via Zermelo navigation. We give a geometric description of the geodesics of the Finsler metric produced from any Finsler metric and any homothetic field in terms of navigation representation, generalizing a result previously only known in the case of Randers metrics with constant S-curvature. As its application, we present explici...

Our main observation concerns closed geodesics on surfaces M with a smooth Finsler metric, i.e. a function F : TM → [0,∞) which is a norm on each tangent space TpM , p ∈ M , which is smooth outside of the zero section in TM , and which is strictly convex in the sense that Hess(F ) is positive definite on TpM \ {0}. One calls a Finsler metric F symmetric if F (p,−v) = F (p, v) for all v ∈ TpM . ...

in this paper, we are going to study the g-natural metrics on the tangent bundle of finslermanifolds. we concentrate on the complex and kählerian and hermitian structures associated with finslermanifolds via g-natural metrics. we prove that the almost complex structure induced by this metric is acomplex structure on tangent bundle if and only if the finsler metric is of scalar flag curvature. t...

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...

in this paper, we study a special class of generalized douglas-weyl metrics whose douglas curvature is constant along any finslerian geodesic. we prove that for every landsberg metric in this class of finsler metrics, ? = 0 if and only if h = 0. then we show that every finsler metric of non-zero isotropic flag curvature in this class of metrics is a riemannian if and only if ? = 0.