In this paper, we study generalized Douglas-Weyl Finsler metrics. We find some conditions under which the class of generalized Douglas-Weyl (&alpha, &beta)-metric with vanishing S-curvature reduce to the class of Berwald metrics.

Every Finsler metric naturally induces a spray but not so for the converse. The notion sprays of scalar (resp. isotropic) curvature has been known as generalization metrics flag curvature. In this paper, new notion, constant curvature, is introduced and especially it shows that isotropic necessarily even in dimension $$n\ge 3$$ . Further, complete conditions are given constant) to be metrizable...

‎the notion of quasi-einstein metric in physics is equivalent to the notion of ricci soliton in riemannian spaces‎. ‎quasi-einstein metrics serve also as solution to the ricci flow equation‎. ‎here‎, ‎the riemannian metric is replaced by a hessian matrix derived from a finsler structure and a quasi-einstein finsler metric is defined‎. ‎in compact case‎, ‎it is proved that the quasi-einstein met...

Locally flat Finsler metrics arise from information geometry. Some speciel locally dually flat Finsler metrics had been studied in Cheng et al. [3] and Xia [4] respectively. As we konw, a new class of Finsler metrics called general (α, β)-metrics are introduced, which are defined by a Riemannian metrics α and 1-form β. These metrics generalize (α, β)-metrics naturally. In this paper, we give a ...

We interpret magnetic billiards as Finsler ones and describe an analog of the string construction for magnetic billiards. Finsler billiards for which the law “angle of incidence equals angle of reflection” are described. We characterize the Finsler metrics in the plane whose geodesics are circles of a fixed radius. This is a magnetic analog of Hilbert’s fourth problem asking to describe the Fin...

This article is an exposition of four loosely related remarks on the geometry of Finsler manifolds with constant positive flag curvature. The first remark is that there is a canonical Kähler structure on the space of geodesics of such a manifold. The second remark is that there is a natural way to construct a (not necessarily complete) Finsler n-manifold of constant positive flag curvature out ...

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...

Methods of estimating (Riemannian and Finsler) filling volumes by using nonexpanding maps to Banach spaces of L∞-type are developed and generalized. For every Finsler volume functional (such as the Busemann volume or the Holmes– Thompson volume), a natural extension is constructed from the class of Finsler metrics to all Lipschitz metrics, and the notion of area is defined for Lipschitz surface...

In Theorem 1, we generalize some results of Szabó [Sz1, Sz2] for Berwald metrics that are not necessarily strictly convex: we show that for every Berwald metric F there always exists a Riemannian metric affine equivalent to F . As an application we show (Corollary 3) that every Berwald projectively flat metric is a Minkowski metric; this statement is a “Berwald” version of Hilbert’s 4th problem...

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 ...