Some general Finsler connections are defined. Emphasis is being made on the Cartan tensor and its derivatives. Vanishing of the hv-curvature tensors of these connections characterizes Landsbergian, Berwaldian as well as Riemannian structures. This view point makes it possible to give a smart representation of connection theory in Finsler geometry and yields to a classification of Finsler connec...

In this paper, we study the Finsler space with special (α, β)-metric is scalar flag curvature and proved that, if it weakly Berwald only vanishes curvature. Further, found that metric locally Minkowskian.

We construct the Extended Relativity Theory in Born-Clifford-Phase spaces with an upper and lower length scales (infrared/ultraviolet cutoff ). The invariance symmetry leads naturally to the real Clifford algebra Cl(2, 6, R) and complexified Clifford ClC(4) algebra related to Twistors. We proceed with an extensive review of Smith’s 8D model based on the Clifford algebra Cl(1, 7) that reproduces...

Munteanu (Complex spaces in Finsler, Lagrange and Hamilton Geometries, Kluwer Academic Publishers, Dordrecht, 2004) defined the canonical connection associated to a strongly pseudoconvex complex Finsler manifold (M, F). We first prove that holomorphic sectional curvature tensors of coincide with those Chern–Finsler F if only is Kähler-Finsler metric. also investigate relationship Ricci curvatur...

In §1 the authors present the basic properties of the scalar product along a curve on a Finsler manifold. In §2 they investigate the variational formulae for the p-energy functional (p ∈ R − {0}). This concept generalises the notions of length (p = 1) and energy (p = 2) of a curve. §3 analyses the extrema of p-energy when the Finsler space has constant curvature. (F3) the fundamental tensor g i...

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, we study a class of finsler metrics which contains the class of p-reducible andgeneral relatively isotropic landsberg metrics, as special cases. we prove that on a compact finsler manifold,this class of metrics is nothing other than randers metrics. finally, we study this class of finsler metrics withscalar flag curvature and find a condition under which these metrics reduce to r...