On almost contact Finsler structures

We introduce almost contact and cosymplectic Finsler manifolds. Then, we characterize almost contact Randers metrics. It is proved that a cosymplectic Finsler manifold of constant flag curvature must have vanishing flag curvature. We prove that every cosymplectic Finsler manifold is a Landsberg space, under a mild condition. Finally, we show that a cosymplectic Finsler manifold is a Douglas space if and only if it is a Berwald space.

Higher rank rigidity for Berwald spaces

We generalize the higher rank rigidity theorem to a class of Finsler spaces, i.e. Berwald spaces. More precisely, we prove that a complete connected Berwald space of finite volume and bounded non-positive flag curvature with rank at least two whose universal cover is irreducible is a locally symmetric space or a locally Minkowski space.

Four-dimensional Conformally Flat Berwald and Landsberg Spaces

The problem of conformal transformation and conformal flatness of Finsler spaces has been studied in [6], [16], [17], [20], [21]. Recently, Prasad et. al [19] have studied three dimensional conformally flat Landsberg and Berwald spaces and have obtained some important results. The purpose of the present paper is to extend the idea of conformal change to four dimensional Finsler spaces and find the suitable conditions under which a four dimensional conformally at Landsberg space becomes a Berwald space.

Projectively Flat Finsler Space of Douglas Type with Weakly-Berwald (α,β)-Metric

The present article is organized as follows: In the first part, we characterize the important class of special Finsler (α,β)-metric in the form ofL=α+α2/β, whereαis Riemannian metric andβis differential 1-form to be projectively flat. In the second part, we describe condition for a Finsler spaceFnwith an (α,β)-metric is of Douglas type. Further we investigate the necessary and sufficient condition for a Finsler space with an (α,β)-metric to be weakly-Berwald space and Berwald space.

On a four-dimensional Berwald space with vanishing h-connection vector $ k_i$

M. Matsumoto and R. Miron [2]$ ^{1)} $ constructed an orthonormal frame for an $ n $-dimensional Finsler space and the frame was called `Miron frame'. T. N. Pandey and D. K. Diwedi [3] and the present authors [4] studied four-dimensional Finsler spaces in terms of scalars. In the present paper, we study a four-dimensional Berwald space with vanishing $ h $-connection vector $ k_i $.