Related papers: On m-th root Finsler metrics
In this paper, we prove that every m-th root metric with isotropic mean Berwald curvature reduces to a weakly Berwald metric. Then we show that an m-th root metric with isotropic mean Landsberg curvature is a weakly Landsberg metric. We…
In this Note, we prove that every m-th root Finsler metric with isotropic Landsberg curvature reduces to a Landsberg metric. Then, we show that every m-th root metric with almost vanishing H-curvature has vanishing H-curvature.
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…
For Finsler spaces (M,F) endowed with m-th root metrics, we provide necessary and sufficient conditions in which they are projectively flat, or projectively related to Berwald/Riemann spaces. We also give a specific characterization for…
In this paper, we consider Kropina change of $m$-th root Finsler metrics. We find necessary and sufficient condition under which the Kropina change of an $m$-th root Finsler metric be locally dually flat. Then we prove that the Kropina…
In this paper we present the m-th root Finsler geometries of the three and four dimensional Bogoslovsky-Goenner metrics (good Finslerian anisotropic models in Special Relativity), in the sense of their Cartan torsion and curvature…
In this paper, we study a class of Finsler metrics which contains the class of Berwald metrics as a special case. We prove that every Finsler metric in this class is a generalized Douglas-Weyl metric. Then we study isotropic flag curvature…
In the current paper, first we give the correct version of the formula for mean Berwald curvature of a spherically symmetric Finsler metric given in paper \cite{YCheWSon2015}. Further, we establish differential equations characterizing…
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.
In this short paper, we establish a closer relation between the Berwald scalar curvature and the $S$-curvature. In fact, we prove that a Finsler metric has isotropic Berwald scalar curvature if and only if it has weakly isotropic…
Let $m=2l$ be a positive natural number, $l=1, 2, \ldots. $ A Finslerian metric $F$ is called an $m$-th root metric if its $m$-th power $F^m$ is of class $C^{m}$ on the tangent manifold $TM$. Using some homogenity properties, the local…
In this paper, we study weakly orthogonally invariant Finsler metrics and derive explicit expressions for their Berwald and Landsberg curvatures. We then obtain the system of partial differential equations characterizing generalized Finsler…
In this paper, we define some non-Riemannian curvature properties for Cartan spaces. We consider Cartan space with the m-th root metric. We prove that every m-th root Cartan space of isotropic Landsberg curvature, or isotropic mean…
In this paper, we study locally projectively flat Finsler metrics with constant flag curvature ${\bf K}$. We prove those are totally determined by their behaviors at the origin by solving some nonlinear PDEs. The classifications when ${\bf…
We study a special class of Finsler metrics which we refer to as Almost Rational Finsler metrics (shortly, AR-Finsler metrics). We give necessary and sufficient conditions for an AR-Finsler manifold $(M,F)$ to be Riemannian. The rationality…
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…
A piecewise flat Finsler metric on a triangulated surface $M$ is a metric whose restriction to any triangle is a flat triangle in some Minkowski space with straight edges. One of the main purposes of this work is to study the properties of…
A Riemannian metric is of constant curvature if and only if it is locally projectively flat. There are infinitely many locally projectively flat Finsler metrics of constant curvature, that are special solutions to the Hilbert's Fourth…
On the product of two Finsler manifolds M1 M2, we consider the twisted metric F which is construct by using Finsler metrics F1 and F2 on the manifolds M1 and M2, respectively. We introduce horizontal and vertical distributions on twisted…
In this paper, we study a new class of Finsler metrics, F=\alpha\phi(b^2,s), s:=\beta/\alpha, defined by a Riemannian metric \alpha and 1-form \beta. It is called general (\alpha, \beta) metric. In this paper, we assume \phi be coefficient…