相关论文: Curvatures on homogeneous Finsler spaces
In this paper, first, we give an explicit formula for the flag curvature of a homogeneous Finsler space with generalized $m$-Kropina metric. Then, we show that, under a mild condition, the two definitions of naturally reductive homogeneous…
In this paper, first we prove the existence of invariant vector field on a homogeneous Finsler space with infinite series $(\alpha, \beta)$-metric and exponential metric. Next, we deduce an explicit formula for the the $S$-curvature of…
The study of curvature properties of homogeneous Finsler spaces with $(\alpha, \beta)$-metrics is one of the central problems in Riemann-Finsler geometry. In the present paper, the existence of invariant vector fields on homogeneous Finsler…
The classification of Finsler spaces of constant curvature is an interesting and important topic of research in differential geometry. In this paper we obtain necessary and sufficient conditions for generalized Kropina space to be of…
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…
In the present article we compute the flag curvature of a special type of invariant Kropina metrics on homogeneous spaces.
In this paper, we first deduce a formula of S-curvature of homogeneous Finsler spaces in terms of Killing vector fields. Then we prove that a homogeneous Finsler space has isotropic S-curvature if and only if it has vanishing S-curvature.…
In this paper, first we derive an explicit formula for the flag curvature of a homogeneous Finsler space with infinite series $(\alpha, \beta)$-metric and exponential metric. Next, we deduce it for naturally reductive homogeneous Finsler…
In this paper, we consider a special class of singular Finsler metrics: $m$-Kropina metrics which are defined by a Riemannian metric and a $1$-form. We show that an $m$-Kropina metric ($m\ne -1$) of scalar flag curvature must be locally…
The study of curvature properties of homogeneous Finsler spaces with $(\alpha, \beta)$-metrics is one of the central problems in Riemann-Finsler geometry. In this paper, we consider homogeneous Finsler spaces with square metric and Randers…
Generalized $m$-Kropina metrics appear naturally as a spacetime geometry compatible with Lorentz symmetry breaking, leading to useful applications in modified gravity and cosmology. We prove that a generalized $m$-Kropina metric $F$ is an…
In this paper, we prove two rigidity results for non-positively curved homogeneous Finsler metrics. Our first main result yields an extension of Hu-Deng's well-known result proven for the Randers metrics. Indeed, we prove that every…
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 give a relationship that yields an effective geometric way of evaluating mean curvature of surfaces. The approach is reminiscent of the Gauss's contour based evaluation of intrinsic curvature. The presented formula may have a number of…
Singular Finsler metrics, such as Kropina metrics and $m$-Kropina metrics, have a lot of applications in the real world. In this paper, we classify a class of singular $(\alpha,\beta)$-metrics which are locally projectively flat with…
In this paper, we give the general form of spherically symmetric Finsler metrics in $R^n$ and surprisedly find that many well-known Finsler metrics belong to this class. Then we explicitly express projective metrics of this type. The…
This is a survey paper on our recent works concerning the classification of positively curved homogeneous Finsler spaces, and some related topics. At the final part, we present some open problems in this field.
In this paper, we study a class of Finsler metrics called general $(\alpha,\beta)$-metrics, which are defined by a Riemannian metric $\alpha$ and a $1$-form $\beta$. We classify this class of Finsler metrics with isotropic Berwald curvature…
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…
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…