The characterization of Finsler spaces of constant curvature is an old and cumbersome one. In the present paper we obtain the conditions for a Kropina space to be of constant curvature improving in this way the characterization given by Matsumoto ([6]) as well as our past results ([13]). M.S.C. 2010: 58B20, 53B21.

In 1977, M. Matsumoto and R. Miron [9] constructed an orthonormal frame for an n-dimensional Finsler space, called ‘Miron frame’. The present authors [1, 2, 3, 10, 11] discussed four-dimensional Finsler spaces equipped with such frame. M. Matsumoto [7, 8] proved that in a three-dimensional Berwald space, all the main scalars are h-covariant constants and the h-connection vector vanishes. He als...

In this paper, we introduce isoparametric functions and hypersurfaces in conic Finsler spaces. We find that there are probably other Minkowski spaces besides the hyperplanes, hyperspheres cylinders, such as helicoids. Moreover, give a complete classification of Kropina with constant flag curvature.

the time-optimal trajectory for an airplane from some starting point to some final point is studied by many authors. here, we consider the extension of robot planer motion of dubins model in three dimensional spaces. in this model, the system has independent bounded control over both the altitude velocity and the turning rate of airplane movement in a non-obstacle space. here, in this paper a g...

Berwald and Wagner manifolds are two important classes of spaces in Finsler geometry. They are closely related to each other via the conformal change of the metric. After discussing the basic definitions and the elements of the theory we present general methods to construct examples of them.

The π-exterior derivative d, which is the Finslerian generalization of the (usual) exterior derivative d of Riemannian geometry, is defined. The notion of a d-closed vector field is introduced and investigated. Various characterizations of d-closed vector fields are established. Some results concerning d-closed vector fields in relation to certain special Finsler spaces are obtained. 1

We propose an approach to the theory of higher order anisotropic field interactions and curved spaces (in brief, ha–field, ha–interactions and ha–spaces). The concept of ha–space generaliSes various types of Lagrange and Finsler spaces and higher dimension (Kaluza–Klein) spaces. This work consists from two parts. In the first we outline the theory of Yang–Mills ha–fields and two gauge models of...