相关论文: Generalized Finsler geometry and its Cartan connec…
Some links between Lorentz and Finsler geometries have been developed in the last years, with applications even to the Riemannian case. Our purpose is to give a brief description of them, which may serve as an introduction to recent…
The aim of the present paper is to investigate new types of recurrence in Finsler geometry, namely, hyper-generalized recurrence and generalized conharmonic recurrence. The properties of such recurrences and their relations to other Finsler…
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…
We discuss the recent proposal of implementing Doubly Special Relativity in configuration space by means of Finsler geometry. Although this formalism leads to a consistent description of the dynamics of a particle, it does not seem to give…
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 is incorporated in the Finslerian structure of space-time. We also…
A common feature of all Quantum Gravity (QG) phenomenology approaches is to consider a modification of the mass shell condition of the relativistic particle to take into account quantum gravitational effects. The framework for such…
Recently we have obtained the Cartan connection for the Finsler space whose metric is given by an exponential change with an h-vector. In this paper, we discuss certain geometric properties of a Finslerian hyperspace subjected to an…
In this work, Einstein's view of geometry as physical geometry is taken into account in the analysis of diverse issues related to the notions of inertial motion and inertial reference frame. Einstein's physical geometry enables a…
The similarity between Finsler and Riemann geometry is an intriguing starting point to extend general relativity. The lack of quadratic restriction over the line element (color) naturally generalize the Riemannian case and breaks the local…
The Finslerian post-Lorentzian kinematic transformations can explicitly be obtained under uni-directional breakdown of spatial isotropy, provided that the requirement that the relativistic unit hypersurface (indicatrix or mass shell) be a…
This article is an exposition of four loosely related remarks on the geometry of Finsler manifolds with constant positive flag curvature. <p> The first remark is that there is a canonical Kahler structure on the space of geodesics of such a…
Along with the construction of non-Lorentz-invariant effective field theories, recent studies which are based on geometric models of Finsler space-time become more and more popular. In this respect, the Finslerian approach to the problem of…
Effective field theories with explicit Lorentz violation are intimately linked to Riemann-Finsler geometry. The quadratic single-fermion restriction of the Standard-Model Extension provides a rich source of pseudo-Riemann-Finsler spacetimes…
This PhD dissertation covers a range of topics in Finsler geometry and Finsler gravity, most notably: (i) the characterization of Berwald spaces, (ii) pseudo-Riemann (non-)metrizability of Berwald spaces, (iii) $(\alpha,\beta)$-metrics,…
First-order general relativity in $n$ dimensions ($n \geq 3$) has an internal gauge symmetry that is the higher-dimensional generalization of three-dimensional local translations. We report the extension of this symmetry for $n$-dimensional…
In this paper, we generalize the classification of geodesic orbit spheres from Riemannian geometry to Finsler geometry. Then we further prove if a geodesic orbit Finsler sphere has constant flag curvature, it must be Randers. It provides an…
This review examines the role of differential forms, Pfaffian systems, and hypersurfaces in general relativity. These mathematical constructions provide the essential tools for general relativity, in which the curvature of…
We consider a triality between the Zermelo navigation problem, the geodesic flow on a Finslerian geometry of Randers type, and spacetimes in one dimension higher admitting a timelike conformal Killing vector field. From the latter…
In this article, we apply the Finsler spacetime to develop the Einstein field equations in the extension of modified geometry. Following Finsler geometry, which is focused on the tangent bundle with a scalar function, a scalar equation…
We present a concise new definition of Finsler spacetimes that generalize Lorentzian metric manifolds and provide consistent backgrounds for physics. Extending standard mathematical constructions known from Finsler spaces we show that…