In this paper, nonholonomic gerbes will be naturally derived for manifolds and vector bundle spaces provided with nonintegrable distributions (in brief, nonholonomic spaces). An important example of such gerbes is related to distributions defining nonlinear connection (N–connection) structures. They geometrically unify and develop the concepts of Riemann–Cartan manifolds and Lagrange–Finsler sp...

The work proposes a general background of the theory of field interactions and strings in spaces with higher order anisotropy. Our approach proceeds by developing the concept of higher order anisotropic superspace which unifies the logical and mathematical aspects of modern Kaluza– Klein theories and generalized Lagrange and Finsler geometry and leads to modelling of physical processes on highe...

the general relatively isotropic mean landsberg metrics contain the general relativelyisotropic landsberg metrics. a class of finsler metrics is given, in which the mentioned two conceptsare equivalent. in this paper, an interpretation of general relatively isotropic mean landsberg metrics isfound by using c-conformal transformations. some necessary conditions for a general relativelyisotropic ...

We study the geometric setting of the field theory with locally anisotropic interactions. The concept of locally anisotropic space is introduced as a general one for various type of extensions of Lagrange and Finsler geometry and higher dimension (Kaluza–Klein type) spaces. The problem of definition of spinors on generalized Finsler spaces is solved in the framework of the geometry of Clifford ...

‎Based on a definition for circle in Finsler space‎, ‎recently proposed by one of the present authors and Z‎. ‎Shen‎, ‎a natural definition of extrinsic sphere in Finsler geometry is given and it is shown that a connected submanifold of a Finsler manifold is totally umbilical and has non-zero parallel mean curvature vector field‎, ‎if and only if its circles coincide with circles of the ambient...

In this paper some geometric structures on Finsler Lie algeboids are studied and h-basic distinguished connections introduced. Specially, Ichijy? connection that is a special investigated. The generalized Berwald algebroids presented, as particular case of Wagner-Ichijy? connection, studied. Moreover, the Wagner algebroid introduced equivalent conditions for space given. Finally, an optimal con...

Given a compact Kahler manifold, the space $\mathcal H$ of its (relative) potentials is an infinite dimensional Frechet on which Mabuchi and Semmes have introduced natural connection $\nabla$. We study certain Lagrangians $T\mathcal H$, in particular Finsler metrics, that are parallel with respect to connection. show geodesics $\nabla$ paths least action, prove convexity property action. This g...

In this paper, we prove a global rigidity theorem for negatively curved Finsler metrics on a compact manifold of dimension n ≥ 3. We show that for such a Finsler manifold, if the flag curvature is a scalar function on the tangent bundle, then the Finsler metric is of Randers type. We also study the case when the Finsler metric is locally projectively flat.