We present an introduction to the geometry of higher order vector and co–vector bundles (including higher order generalizations of the Finsler geometry and Kaluza– Klein gravity) and review the basic results on Clifford and spinor structures on spaces with generic local anisotropy modeled by anholonomic frames with associated nonlinear connection structures. We emphasize strong arguments for ap...

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 ...

We propose an unified approach to loop quantum gravity and Fedosov quantization of gravity following the geometry of double spacetime fibrations and their quantum deformations. There are considered pseudo–Riemannian manifolds enabled with 1) a nonholonomic 2+2 distribution defining a nonlinear connection (N–connection) structure and 2) an Arnowitt–Deser–Misner 3+1 decomposition. The Ashtekar– B...

in this paper the general relatively isotropic l -curvature finsler metrics are studied. it isshown that on constant relatively landsberg spaces, the concepts of weakly landsbergian, landsbergianand generalized landsbergian metrics are equivalent. some necessary conditions for a relativelyisotropic l -curvature finsler metric to be a riemannian metric are also found.

Locally flat Finsler metrics arise from information geometry. Some speciel locally dually flat Finsler metrics had been studied in Cheng et al. [3] and Xia [4] respectively. As we konw, a new class of Finsler metrics called general (α, β)-metrics are introduced, which are defined by a Riemannian metrics α and 1-form β. These metrics generalize (α, β)-metrics naturally. In this paper, we give a ...

From a rigorous Finsler geometric perspective, we re-examine Holland’s Randers space theory of motion of an electron in flat Minkowski spacetime permeated with an electromagnetic field. Holland’s theory was motivated by analogy with plastic deformation and dislocation in Bravais crystals, through work of D. Bohm on Quantum Mechanics. We develop the anholonomic geometry of a Randers space using ...

A geometric procedure is elaborated for transforming (pseudo) Riemanian metrics and connections into canonical geometric objects (metric and nonlinear and linear connections) for effective Lagrange, or Finsler, geometries which, in their turn, can be equivalently represented as almost Kähler spaces. This allows us to formulate an approach to quantum gravity following standard methods of deforma...

In this paper we extend the study of the indicatrix of a complex Finsler space initiated in [10, 11]. The equations that can be introduced on the indicatrix, which is studied as a hypersurface of a complex Finsler space, are investigated. In this manner, using the equations of Gauss-Weingarten, the link between the intrinsic and induced connection is deduced. The equations of Gauss, H -and A-Co...

We propose a natural Fedosov type quantization of generalized Lagrange models and gravity theories with metrics lifted on tangent bundle, or extended to higher dimension, following some stated geometric/ physical conditions (for instance, nonholonomic and/or conformal transforms to some physically important metrics or mapping into a gauge model). Such generalized Lagrange transforms define cano...