It is shown that the projectivised tangent bundle of Finsler spaces with the Chern connection has a contact metric structure under a conformal transformation with certain condition of the Finsler function and moreover it is locally isometric to E × Sm−1(4) for m > 2 and flat for m = 2 if and only if the Cartan tensor vanishes, i.e., the Finsler space is a Riemannian manifold. M.S.C. 2000: 53C60...

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...

Abstract We extend the treatment of quantum cosmology to a manifold with torsion. adopt model Einstein-Cartan-Sciama-Kibble compatible cosmological principle. The universe wave function is shown be subject . With vanishing energy-momentum tensor, evolution in semiclassical and classical regimes suggest two-stage inflationary process induced...

It is fairly well known that rotation in three dimensions can be expressed as a quadratic in a skew symmetric matrix via the Euler-Rodrigues formula. A generalized Euler-Rodrigues polynomial of degree 2n in a skew symmetric generating matrix is derived for the rotation matrix of tensors of order n. The Euler-Rodrigues formula for rigid body rotation is recovered by n = 1. A Cayley form of the n...

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...

Riemannian geometry has become a popular mathematical framework for the analysis of diffusion tensor images (DTI) in diffusion weighted magnetic resonance imaging (DWMRI). If one declines from the a priori constraint to model local anisotropic diffusion in terms of a 6-degrees-of-freedom rank-2 DTI tensor, then Riemann-Finsler geometry appears to be the natural extension. As such it provides an...

In this paper, we construct a single Lagrangian for both limits of Galilean electrodynamics. The framework relies on covariant formalism used in describing Newton-Cartan geometry. We write down the conformal algebra and its representation formalism. also show that is invariant under d = 4 calculate energy-momentum tensor.

A general geometric construction of a generic null hypersurface in presence torsion the spacetime (Riemann-Cartan background), generated by vector ${l}^{a}$, is being developed here. We then explicitly define and structure various corresponding kinematical quantities. The dynamics surface, particularly given ${\stackrel{^}{G}}_{ab}{k}^{a}{l}^{b}$, also discussed. later one constructed under geo...

Starting from compact symmetric spaces of inner type, we provide infinite families homogeneous carrying invariant non-flat Bismut connections with vanishing Ricci tensor. These examples turn out to be generalized order [Formula: see text] and (up coverings) they can realized as minimal submanifolds the flat model spaces, namely Lie groups. This construction generalizes standard Cartan embedding...