In this paper, we prove that for every Finsler metric on S there exist at least two distinct prime closed geodesics. For the case of the two-sphere, this solves an open problem posed by D. V. Anosov in 1974.

Berwald metrics are particular Finsler metrics which still have linear Berwald connections. Their complete classification is established in an earlier work, [Sz1], of this author. The main tools in these classification are the Simons-Berger holonomy theorem and the Weyl-group theory. It turnes out that any Berwald metric is a perturbed-Cartesian product of Riemannian, Minkowski, and such non-Ri...

A particular Finsler-metric proposed in [1,2] and describing a geometry with a preferred null direction is characterized here as belonging to a subclass contained in a larger class of Finsler-metrics with one or more preferred directions (null, spaceor timelike). The metrics are classified according to their group of isometries. These turn out to be isomorphic to subgroups of the Poincaré (Lore...

In this paper, we prove that for every Finsler metric on S there exist at least two distinct prime closed geodesics. For the case of the two-sphere, this solves an open problem posed by D. V. Anosov in 1974.

We consider the p–Laplacian operator on a domain equipped with a Finsler metric. We recall relevant properties of its first eigenfunction for finite p and investigate the limit problem as p → ∞.

There are two definitions of Einstein-Finsler spaces introduced by Akbar-Zadeh, which we will show is equal along the integral curves $I$-invariant projective vector fields. The sub-algebra $C$-projective fields, leaving $H$-curvature invariant, has been studied extensively. Here on a closed Finsler space with negative definite Ricci curvature reduces to that Killing Moreover, if an admits such...

In this essay, we study the sufficient and necessary conditions for a Randers metrc to be of constant Ricci curvature, without the restriction of strong convexity (regularity). A classification result for the case ‖β‖α > 1 is provided, which is similar to the famous Bao-Robles-Shen’s result for strongly convex Randers metrics (‖β‖α < 1). Based on some famous vacuum Einstein metrics in General R...

The paper generalises Thompson and Hilbert metric to the space of spectral densities. The resulting complete metric space has the differentiable structure of a Finsler manifold with explicit geodesics. Additionally, in the rational case, the resulting distance is filtering invariant and can be computed efficiently.

The purpose of the present paper is to investigate the various kinds of hypersurfaces of Finsler space with special (α, β) metric α + β n+1 αn which is a generalization of the metric α+ β 2 α consider in [9]. 2000 Mathematics Subject Classification: 53B40, 53C60.

This paper studies the space of BV 2 planar curves endowed with the BV 2 Finsler metric over its tangent space of displacement vector fields. Such a space is of interest for applications in image processing and computer vision because it enables piecewise regular curves that undergo piecewise regular deformations, such as articulations. The main contribution of this paper is the proof of the ex...