Related papers: Finsler metrics and semi-symmetric compatible line…
A Randers space is a differentiable manifold equipped with a Randers metric. It is the sum of a Riemannian metric and a one-form on the base manifold. The compatibility of a linear connection with the metric means that the parallel…
Munteanu defined the canonical connection associated to a strongly pseudoconvex complex Finsler manifold $(M,F)$. We first prove that the holomorphic sectional curvature tensors of the canonical connection coincide with those of the…
Given a Finsler space (M,F) on a manifold M, the averaging method associates to Finslerian geometric objects affine geometric objects} living on $M$. In particular, a Riemannian metric is associated to the fundamental tensor $g$ and an…
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…
In this paper, studying the inverse problem, we establish a curvature compatibility condition on a spherically symmetric Finsler metric. As an application, we characterize the spherically symmetric metrics of scalar curvature. We construct…
We provide a functional characterization of isometries between non-reversible Finsler manifolds, in the form of a generalization of the Myers-Nakai Theorem for Riemannian manifolds. We show that, since non-reversible Finsler manifolds are a…
In the standard approach to Finsler geometry the metric is defined as a vertical Hessian and the Chern or Cartan connections appear as just two among many possible natural linear connections on the pullback tangent bundle. Here it is shown…
By using a certain second order differential equation, the notion of adapted coordinates on Finsler manifolds is defined and some classifications of complete Finsler manifolds are found. Some examples of Finsler metrics, with positive…
Special coordinate systems are constructed in a neighborhood of a point or of a curve. Taylor expansions can then be easily inferred for the metric, the connection, or the Finsler Lagrangian in terms of curvature invariants. These…
Finsleroid-Finsler metrics form an important class of singular (y-local) Finsler metrics. They were introduced by G. S. Asanov [2] in 2006. As the special case of the general construction Asanov produced singular (y - local) examples of…
For a torsion-free affine connection on a given manifold, which does not necessarily arise as the Levi-Civita connection of any pseudo-Riemannian metric, it is still possible that it corresponds in a canonical way to a Finsler structure;…
This paper is devoted to the study of the T-tensor associated with a spherically symmetric Finsler metric $F=u\phi(r,s)$ on \(\mathbb{R}^n\). We derive a general expression for the T-tensor in terms of the scalar function \(\phi(r, s)\) and…
We prove existence of harmonic coordinates for the nonlinear Laplacian of a Finsler manifold and apply them in a proof of the Myers--Steenrod theorem for Finsler manifolds. Different from the Riemannian case, these coordinates are not…
There were elaborated different models of Finsler geometry using the Cartan (metric compatible), or Berwald and Chern (metric non-compatible) connections, the Ricci flag curvature etc. In a series of works, we studied (non)commutative…
In this paper, we explore the similarity between normal homogeneity and $\delta$-homogeneity in Finsler geometry. They are both non-negatively curved Finsler spaces. We show that any connected $\delta$-homogeneous Finsler space is…
In this paper, as an application of the inverse problem of calculus of variations, we investigate two compatibility conditions on the spherically symmetric Finsler metrics. By making use of these conditions, we focus our attention on the…
The general notion of anisotropic connections $\nabla$ is revisited, including its precise relations with the standard setting of pseudo-Finsler metrics, i.e., the canonic nonlinear connection and the (linear) Finslerian connections. In…
It is shown that a possibly irreversible $C^2$ Finsler metric on the torus, or on any other compact Euclidean space form, whose geodesics are straight lines is the sum of a flat metric and a closed $1$-form. This is used to prove that if…
The aim of the present paper is to provide a global presentation of the theory of special Finsler manifolds. We introduce and investigate globally (or intrinsically, free from local coordinates) many of the most important and most commonly…
We briefly review some basic concepts of parallel displacement in Finsler geometry. In general relativity, the parallel translation of objects along the congruence of the fundamental observer corresponds to the evolution in time. By…