Related papers: A metrical approach to Finsler geometry
Let $R$ be the $hh$-curvature associated with the Chern connection or the Cartan connection. Adopting the pulled-back tangent bundle approach to the Finslerian Geometry, an intrinsic characterization of $R$-Einstein metrics is given.…
The generalized Finsler geometry, as well as Finsler geometry, is a generalization of Riemann geometry. The generalized Finsler geometry can be endowed with the Cartan connection. The generalized Finsler geometry and its Cartan connection…
The aim of the present paper is to provide an \emph{intrinsic} investigation of the properties of the most important geometric objects associated with the fundamental linear connections in Finsler geometry. We investigate intrinsically the…
I do not agree with the authors of papers arXiv:0806.2184 and arXiv:0901.1023v1 (published in Phys. Lett., respectively, B668 (2008) 453 and B676 (2009) 173). They consider that \textit{"In Finsler manifold, there exists a unique linear…
Adopting the pullback approach to global Finsler geometry, the aim of the present paper is to provide intrinsic (coordinate-free) proofs of the existence and uniqueness theorems for the Chern (Rund) and Hashiguchi connections on a Finsler…
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…
We study the geometric and physical foundations of Finsler gravity theories with metric compatible connections defined on tangent bundles, or (pseudo) Riemannian manifolds). There are analyzed alternatives to Einstein gravity (including…
We give a Finsler non-linear connection by a new simplified definition for not only regular case but also singular case. In regular case, it corresponds to non-linear connection part of Berwald's connection, but our connection is expressed…
In this article, we review the current status of Finsler-Lagrange geometry and generalizations. The goal is to aid non-experts on Finsler spaces, but physicists and geometers skilled in general relativity and particle theories, to…
Modern formulation of Finsler geometry of a manifold M utilizes the equivalence between this geometry and the Riemannian geometry of VTM, the vertical bundle over the tangent bundle of M, treating TM as the base space. We argue that this…
We construct gravitational dynamics for Finsler spacetimes in terms of an action integral on the unit tangent bundle. These spacetimes are generalizations of Lorentzian metric manifolds which satisfy necessary causality properties. A…
Under a pulled-back approach given in [1] and firstly presented in [2], we introduce, in this paper, the concepts of almost contact and normal almost contact Finsler structures on the pulled-back bundle. Properties of structures partly…
The appearance of two geometries in one and the same gravitational theory is familiar. Usually, as in the Brans-Dicke theory or in string theory, these are conformally related Riemannian geometries. Is this the most general relation between…
We propose a natural Fedosov type quantization of generalized Lagrange models and gravity theories with metrics lifted on tangent bundle, or extended to higher dimension, following some stated geometric/ physical conditions (for instance,…
A geodesic circle in Finsler geometry is a natural extension of that in a Euclidean space. In this paper, we apply Lie derivatives and the Cartan $Y$-connection to study geodesic circles and (infinitesimal) concircular transformations on a…
We analyze the foundations of Finsler gravity theories with metric compatible connections constructed on nonholonomic tangent bundles, or (pseudo) Riemannian manifolds. There are considered "minimal" modifications of Einstein gravity…
In this paper we describe an approach to complex Finsler metrics suitable to deal with global questions, and stressing the similarities between hermitian and complex Finsler metrics. Let $F$ be a smooth complex Finsler metric on a complex…
We develop the method of anholonomic frames with associated nonlinear connection (in brief, N--connection) structure and show explicitly how geometries with local anisotropy (various type of Finsler--Lagrange--Cartan--Hamilton geometry) can…
Finsler metrics are direct generalizations of Riemannian metrics such that the quadratic Riemannian indicatrices in the tangent spaces of a manifold are replaced by more general convex bodies as unit spheres. A linear connection on the base…
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…