Class Of Finsler Spaces Research Articles

Average of geometric structures in Finsler spaces with Lorentzian signature

Given the class of Finsler spaces with Lorentzian signature [Formula: see text] on a manifold [Formula: see text] endowed with a timelike vector field [Formula: see text] satisfying [Formula: see text] at any point [Formula: see text] of the slit tangent bundle, a pseudo-Riemannian metric defined on [Formula: see text] of signature [Formula: see text] is associated to the fundamental tensor [Formula: see text]. Furthermore, an affine, torsion free connection is associated to the Chern connection determined by [Formula: see text]. The definition of the average connection does not make use of [Formula: see text]. Therefore, there is no direct relation between these two averaged objects.

A class of Finsler spaces with general (α,β)-metrics

In the present paper, we prove that a general [Formula: see text]-metric [Formula: see text] is of isotropic [Formula: see text]-curvature if and only if it is of isotropic [Formula: see text]-curvature under an extra condition on [Formula: see text] and [Formula: see text].

New class of Finsler metrics

A class of Finsler spaces is introduced which is determined by the metric functionF(x, y)=[ηαβ +kBαBβ)yαyβ]1/2, whereBα =Bαx, y andk is a constant. Various properties of these spaces are developed. A particular choice ofBα is shown to produce a geodesic equation which is equivalent to the Lorentz equation of motion for a charged particle. Some general arguments for the physical applicability of Finsler spaces are also given.