Related papers: On almost rational Finsler metrics

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…

If the flag curvature of a Finsler manifold reduces to sectional curvature, then locally either the Finsler metric is Riemannian, or the flag curvature is isotropic.

Finsler metrics of scalar flag curvature play an important role to show the complexity and richness of general Finsler metrics. In this paper, on an $n$-dimensional manifold $M$ we study the Finsler metric $F=F(x,y)$ of scalar flag…

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 this essay, we study the sufficient and necessary conditions for a Randers metrc to be of constant Ricci curvature without the restriction of strong convexity (regularity). The classification result for the case $\|\beta\|_{\alpha}>1$ is…

We undertake to show how the relativistic Finslerian Metric Function (FMF) should arise under uni-directional violation of spatial isotropy, keeping the condition that the indicatrix (mass-shell) is a space of constant negative curvature.…

Let (M1,F1) and (M2,F2) be two Finsler manifolds. The twisted product Finsler metric of F1 and F2 is a Finsler metric F = (F1^2+ f^2F2^2)^1/2 endowed on the product manifold M1 * M2, where f is a positive smooth function on M1 * M2. In this…

Weighted Ricci curvatures with various weights of the S-curvature have played an important role in Finsler geometry, especially in the control of volumes of Finsler manifolds. In this paper, we study general weighted Ricci curvatures, and…

In the present paper, we introduce and investigate various types of harmonic Finsler manifolds and find out the interrelation between them. We give some characterizations of such spaces in terms of the mean curvature of geodesic spheres and…

The Ricci version of the Schur theorem is shown to hold for a wide class of Finsler metrics. What is more, let $F$ be any (positive definite) Finsler metric such that $\text{Ric} =\rho F^2$ with $\rho\colon M^n\rightarrow\mathbb{R}$ (i.e.,…

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…

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…

In this paper, we introduce the weighted projective Ricci curvature as an extension of projective Ricci curvature introduced by Z. Shen. We characterize the class of Randers metrics of weighted projective Ricci flat curvature. We find the…

We determine all Finsler metrics of Randers type for which the Riemannian part is a scalar multiple of the Euclidean metric, on an open subset of the Euclidean plane, whose geodesics are circles. We show that the Riemannian part must be of…

We show that the second greatest possible dimension of the group of (local) almost isometries of a Finsler metric is $\frac{n^2 -n}{2} +1$ for $n= dim(M)\ne 4 $ and $\frac{n^2 -n}{2} +2 =8$ for $n=4$. If a Finsler metric has the group of…

In the present paper, we find out necessary and sufficient conditions for a Finsler surface $(M,F)$ to be Landsbregian in terms of the Berwald curvature $2$-forms. We study Finsler surfaces which satisfy some flag curvature $K$ conditions,…

We show that in dimension 2 every Finsler metric with at least 3-dimensional Lie algebra of projective vector fields is locally projectively equivalent to a Randers metric. We give a short list of such Finsler metrics which is complete up…

For every Finsler metric $F$ we associate a Riemannian metric $g_F$ (called the Binet-Legendre metric). The transformation $F \mapsto g_F$ is $C^0$-stable and has good smoothness properties, in contrast to previous constructions. The…

This manuscript investigates the curvature and topological properties of certain $\infty$-Einstein Finsler metrics on Finsler metric measure spaces. By imposing symmetry conditions, we construct a series of special metrics and analyze their…

In this paper, we characterize locally dually flat generalized m-th root Finsler metrics. Then we find a condition under which a generalized m-th root metric is projectively related to a m-th root metric. Finally, we prove that if a…