It is shown that the projectivised tangent bundle of Finsler spaces with the Chern connection has a contact metric structure under a conformal transformation with certain condition of the Finsler function and moreover it is locally isometric to E × Sm−1(4) for m > 2 and flat for m = 2 if and only if the Cartan tensor vanishes, i.e., the Finsler space is a Riemannian manifold. M.S.C. 2000: 53C60...

We study non-reversible Finsler metrics with constant flag curvature 1 on S and show that the geodesic flow of every such metric is conjugate to that of one of Katok’s examples, which form a 1-parameter family. In particular, the length of the shortest closed geodesic is a complete invariant of the geodesic flow. We also show, in any dimension, that the geodesic flow of a Finsler metrics with c...

A Finsler metric is of sectional flag curvature if its flag curvature depends only on the section. In this article, we characterize Randers metrics of sectional flag curvature. It is proved that any non-Riemannian Randers metric of sectional flag curvature must have constant flag curvature if the dimension is greater than two. 0. Introduction Finsler geometry has a long history dated from B. Ri...

The well-known invariants of conics are computed for classes of Finsler and Lagrange spaces. For the Finsler case, some (α, β)-metrics namely Randers, Kropina and ”Riemann”-type metrics provides conics as indicatrices and a Randers-Funk metric on the unit disk is treated as example. The relations between algebraic and differential invariants of (α, β)-metrics are pointed out as a method to use ...

In 1984 C.Shibata has dealt with a change of Finsler metric which is called a β-change of metric [12]. For a β-change of Finsler metric, the differential oneform β play very important roles. In 1985 M.Matsumoto studied the theory of Finslerian hypersurfaces [6]. In there various types of Finslerian hypersurfaces are treated and they are called a hyperplane of the 1st kind, a hyperplane of the 2...

One of the key properties of the length of a curve is its lower semicontinuity : if a sequence of curves γi converges to a curve γ, then length(γ) ≤ lim inf length(γi). Here the weakest type of pointwise convergence suffices. There are higher-dimensional analogs of this semicontinuity for Riemannian (and even Finsler) metrics. For instance, the Besicovitch inequality (see, e.g., [1] and [4]) im...

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 ...

Asking that the metric of a complex Finsler space should be strong convex, Abate and Patrizio ([1]) associate to the real tangent bundle a real Finsler metric for which they analyze the relation between Cartan (real) connection of the obtained space and the real image of Chern-Finsler complex connection. Following the same ideas, in the present paper we shall deal with the more general case of ...

In this paper we introduce the class of R-complex Finsler spaces with (α, β)-metrics and study some important exemples: R-complex Randers spaces, R-complex Kropina spaces. The metric tensor field of a R-complex Finsler space with (α, β)-metric is determined (§2). A special approach is dedicated to the R-complex Randers spaces (§3). AMS Mathematics Subject Classification (2000): 53B40, 53C60

The dual flatness for Riemannian metrics in information geometry has been extended to Finsler metrics. The aim of this paper is to study the dual flatness of the so-called (α, β)-metrics in Finsler geometry. By doing some special deformations, we will show that the dual flatness of an (α, β)-metric always arises from that of some Riemannian metric in dimensional n ≥ 3.