Adopting the pullback approach to Finsler geometry, the aim of the present paper is to provide new intrinsic (coordinate-free) proofs of intrinsic versions of the existence and uniqueness theorems for the Cartan and Berwald connections on a Finsler manifold. To accomplish this, the notions of semispray and nonlinear connection associated with a given regular connection, in the pullback bundle, ...

On a Finsler manifold (M,L), we consider the change L −→ L(x, y) = eL(x, y) + β(x, y), which we call a β-conformal change. This change generalizes various types of changes in Finsler geometry: conformal, C-conformal, h-conformal, Randers and generalized Randers changes. Under this change, we obtain an explicit expression relating the Cartan connection associated to (M,L) and the transformed Car...

In this paper we investigate the spectral problem in Finsler geometry. Due to nonlinearity of Finsler–Laplacian operator, introduce faithful dimension pairs by means which spectrum a compact reversible metric measure manifold is defined. Various upper and lower bounds such eigenvalues are provided spirit Cheng, Buser Gromov, extend several aspects results Hassannezhad, Kokarev Polterovich. More...

The objective of this article is to build up a general theory of geometrical optics for spinning light rays in an inhomogeneous and anisotropic medium modeled on a Finsler manifold. The prerequisites of local Finsler geometry are reviewed together with the main properties of the Cartan connection used in this work. Then, the principles of Finslerian spinoptics are formulated on the grounds of p...

we establish some relative volume comparison theorems for extremal volume forms of‎ ‎finsler manifolds under suitable curvature bounds‎. ‎as their applications‎, ‎we obtain some results on curvature and topology of finsler manifolds‎. ‎our results remove the usual assumption on s-curvature that is needed in the literature‎.

Let X be a Finsler manifold. We prove some abstract results on the existence of critical points for strongly indefinite functionals f ∈ C1(X ,R) via a new deformation theorem. Different from the works in the literature, the new deformation theorem is constructed under a new version of Cerami-type condition instead of Palais-Smale condition. As applications, we prove the existence of multiple pe...

Let M be a differentiable manifold, T x its tangent space at ε and TM={(x,y);x M; y M} bundle. A C 0 -Finsler structure is continuous function F:TM → [0, ∞ ) such that F(x, · ):T an asymmetric norm. In this work we introduce the Pontryagin type structures, which are structures satisfy minimum requirements of Pontryagin's maximum principle for problem minimizing paths. We define extended geodesi...