Related papers: On dually flat general $(\alpha,\beta)$-metrics

In this paper, I will show how to use $\beta$-deformations to deal with dual flatness of $(\alpha,\beta)$-metrics. It is a natural continuation of the research on dually flat Randers metrics(see arxiv:1209.1150). $\beta$-deformations is a…

In this paper we study the flag curvature of a particular class of Finsler metrics called general $(\alpha,\beta)$-metrics, which are defined by a Riemannian metric $\alpha$ and a $1$-form $\beta$. The classification of such metrics with…

In this paper, we study a class of Finsler metrics composed by a Riemann metric $\alpha=\sqrt{a_{ij}(x)y^i y^j}$ and a $1$-form $\beta=b_i(x)y^i$ called general ($\alpha$, $\beta$)-metrics. We classify those projectively flat when $\alpha$…

In this paper, we study a class of two-dimensional Finsler metrics defined by a Riemannian metric $\alpha$ and a 1-form $\beta$. We characterize those metrics which are Douglasian or locally projectively flat by some equations. In…

In this paper, a new class of Finsler metrics which are included $(\alpha,\beta)$-metrics are introduced. They are defined by a Riemannian metric and two 1-forms $\beta=b_i(x)y^i$ and $\gamma= \gamma_i(x)y^i$. This class of metrics are a…

In this paper, I will show how to use beta-deformations to deal with dual flatness of Randers metrics. beta-deformations is a new method in Riemann-Finsler geometry, it is introduced by the author(see arxiv:1209.0845). Later on I will…

In this paper, the geometric meaning of (alpha,beta)-norms is made clear. On this basis, we introduce a new class of Finsler metrics called general (alpha,beta)-metrics, which are defined by a Riemannian metric and an 1-form. These metrics…

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 find an equation which is necessary and sufficient condition for such…

The class of spherically symmetric Finsler metrics is studied and locally dually flat and projectively flat spherically symmetric Finsler metrics is classified.

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 consider Randers change of some special $ (\alpha, \beta)- $ metrics. First we find the fundamental metric tensor and Cartan tensor of these Randers changed $ (\alpha, \beta)- $metrics. Next, we establish a general formula…

In this paper, we study a special class of Finsler metrics, $(\alpha,\beta)$-metrics, defined by $F = \alpha \phi(\frac{\beta}{\alpha})$, where $\alpha$ is a Riemannian metric and $\beta$ is a 1-form. We find an equation that characterizes…

The emergence of generalized square metrics in Finsler geometry can be attributed to various classification concerning ({\alpha}, \beta})-metrics. They have excellent geometric properties in Finsler geometry. Within the scope of this…

In this paper, we study almost regular Landsberg general $(\alpha,\beta)$-metrics in Finsler geometry. The corresponding equivalent equations are given. By solving the equations, we give the classification of Landsberg general…

In this paper, the Douglas curvature of (\alpha,\beta)-metrics, a special class of Finsler metrics defined by a Riemannian metric \alpha and a 1-form \beta, is studied. These metrics with vanishing Douglas curvature in dimension n\geq3 are…

Douglas metrics are metrics with vanishing Douglas curvature which is an important projective invariant in Finsler geometry. To find more Douglas metrics, in this paper we consider a class of Finsler metrics called general…

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…

In this paper, we study a class of Finsler metrics called general (\alpha,\beta)-metrics, which are defined by a Riemannian metric and an 1-form. We construct some general (\alpha,\beta)-metrics with constant Ricci curvature.

In this paper, we introduce and investigate a general transformation or change of Finsler metrics, which is referred to as a generalized $\beta$-conformal change: $$L(x,y) \longrightarrow\overline{L}(x,y) =…

In this paper, we give the flag curvature formula of general $(\alpha,\beta)$-metrics of Berwald type. We study conformally related $(\alpha,\beta)$-metrics, especially general $(\alpha,\beta)$-metrics that are conformally related to…