Two special Finsler spaces have been introduced and investigated, namely R-recurrent Finsler space and concircularly recurrent Finsler space. The defining properties of these spaces are formulated in terms of the first curvature tensor of Cartan connection. The following three results constitute the main object of the present paper: (i) a concircularly flat Finsler manifold is necessarily of co...

When Einstein was thinking about the theory of general relativity based on the elimination of especial relativity constraints (especially the geometric relationship of space and time), he understood the first limitation of especial relativity is ignoring changes over time. Because in especial relativity, only the curvature of the space was considered. Therefore, tensor calculations should be to...

In this note we give sufficient conditions to ensure that the weak Finsler structure of a complete C Finsler manifold M is determined by the normed algebra C b (M) of all real-valued, bounded and C k smooth functions with bounded derivative defined on M . As a consequence, we obtain: (i) the Finsler structure of a finite-dimensional and complete C Finsler manifold M is determined by the algebra...

In this paper, it is elaborated the theory the Ricci flows for manifolds enabled with nonintegrable (nonholonomic) distributions defining nonlinear connection structures. Such manifolds provide a unified geometric arena for nonholonomic Riemannian spaces, Lagrange mechanics, Finsler geometry, and various models of gravity (the Einstein theory and string, or gauge, generalizations). We follow th...

It is shown that the problem of a possible violation of the Lorentz transformations at Lorentz factors γ > 5×10 10 , indicated by the situation which has developed in the physics of ultra-high energy cosmic rays (the absence of the GZK cutoff), has a nontrivial solution. Its essence consists in the discovery of the so-called generalized Lorentz transformations which seem to correctly link the i...

Lagrange geometry is the geometry of the tensor field defined by the fiberwise Hessian of a non degenerate Lagrangian function on the total space of a tangent bundle. Finsler geometry is the geometrically most interesting case of Lagrange geometry. In this paper, we study a generalization, which consists of replacing the tangent bundle by a general tangent manifold, and the Lagrangian by a fami...

We study stationary configurations mimicking nonholonomic locally anisotropic black rings (for instance, with ellipsoidal polarizations and/or imbedded into solitonic backgrounds) in three/six dimensional pseudo–Finsler/ Riemannian spacetimes. In the asymptotically flat limit, for holonomic configurations, a subclass of such spacetimes contains the set of five dimensional black ring solutions w...

We model pseudo–Finsler geometries, with pseudo–Euclidean signatures of metrics, for two classes of four dimensional nonholonomic manifolds: a) tangent bundles with two dimensional base manifolds and b) pseudo–Riemannian/ Einstein manifolds. Such spacetimes are enabled with nonholonomic distributions and associated nonlinear connection structures and theirs metrics are solutions of the field eq...

In this note the geometry of the indicatrix (I, L̃) is studied as a hypersurface of a complex Finsler space (M,L). The induced Chern-Finsler and Berwald connections are defined and studied. The induced Berwald connection coincides with the intrinsic Berwald connection of the indicatrix bundle. We considered a special projection of a geodesic curve on a complex Finsler space (M,L), called the ind...