In this paper, we obtain extensions of majorization type results and extensions of weighted Favard’s and Berwald’s inequality. We prove positive semi-definiteness of matrices generated by differences deduced from majorization type results and differences deduced from weighted Favard’s and Berwald’s inequality. This implies a surprising property of exponentially convexity and log-convexity of th...

In this paper, we study the set of homogeneous geodesics of a leftinvariant Finsler metric on Lie groups. We first give a simple criterion that characterizes geodesic vectors. As an application, we study some geometric properties of bi-invariant Finsler metrics on Lie groups. In particular a necessary and sufficient condition that left-invariant Randers metrics are of Berwald type is given. Fin...

Using the Blaschke-Berwald metric and affine shape operator of a hypersurface M in (n+1)-dimensional real space we can define some generalized curvature tensor named Opozda-Verstraelen tensor. In this paper determine conditions pseudosymmetry type expressed by for locally strongly convex hypersurfaces M, n>2, with two distinct principal curvatures or three assuming that at least one has multipl...

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...

Finsler geometry is a natural and fundamental generalization of Riemann geometry. The Finsler structure depends on both coordinates and velocities. It is defined as a function on tangent bundle of a manifold. We use the Bianchi identities satisfied by Chern curvature to set up a gravitation theory in Berwald-Finsler space. The geometric part of the gravitational field equation is nonsymmetric i...