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 ...

The specific astrophysical data collected during the last decade causes the need for the modification of the expression for the Einstein-Hilbert action, and several attempts sufficing this need are known. The modification suggested in this paper stems from the possible anisotropy of space-time and this means the natural change of the simplest scalar in the least action principle. To provide the...

Kinematic and geometrical aspects of the connection between energy and inertial mass are considered. Transformations of coordinate and time are obtained in a two-dimensional flat space. For this case the Euclidean, pseudo-Euclidean and Galilean kinematics are considered. A new interval in a flat fourdimensional anisotropic Finsler space is found. Under certain assumptions the known results foll...

In this work we study an anisotropic model of general relativity based on the framework of Finsler geometry. The observed anisotropy of the microwave background radiation [8] is incorporated in the Finslerian structure of space-time. We also examine the electromagnetic (e.m.) field equations in our space. As a result a modified wave equation of e.m. waves yields.

The book “Handbook of Finsler geometry” has been included with a CD containing an elegant Maple package, FINSLER, for calculations in Finsler geometry. Using this package, an example concerning a Finsler generalization of Einstein’s vacuum field equations was treated. In this example, the calculation of the components of the hv-curvature of Cartan connection leads to wrong expressions. On the o...

Lagrange geometry is the geometry of the tensor field defined by the fiberwise Hessian of a nondegenerate Lagrangian function on the total space of a tangent bundle. Finsler geometry is the geometrically most interesting case of Lagrange geometry. In this paper, we study a generalization which consists of replacing the tangent bundle by a general tangent manifold, and the Lagrangian by a family...

‎In this article we review an algebraic definition of the gyrogroup and a simplified version of the gyrovector space with two fundamental examples on the open ball of finite-dimensional Euclidean spaces‎, ‎which are the Einstein and M"{o}bius gyrovector spaces‎. ‎We introduce the structure of gyrovector space and the gyroline on the open convex cone of positive definite matrices and explore its...