Related papers: Generalized Isotropic Berwald Manifolds

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…

This paper introduces a new quantity in Finsler geometry, called the generalized Berwald projective Weyl ($GB\widetilde{W}$) metric. The $C$-projective invariance of these metrics is demonstrated, and it is shown that they constitute a…

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…

The class of generalized Berwald metrics contains the class of Berwald metrics. In this paper, we characterize two-dimensional generalized Berwald $(\alpha, \beta)$-metrics with vanishing S-curvature. Let $F=\alpha\phi(s)$,…

In this paper, we classify the spherically symmetric Berwald metrics in $\mathbb{R}^n$. For the spherically symmetric Landsberg metrics, we prove that there do not exist any non-Berwald metrics among the regular case. The partial…

We prove that every Berwald manifold with non-zero flag curvature is Riemannian. This result provides an extension of Numata and Szabo's rigidity theorems. We show that every positively curved constant isotropic Berwald manifold is…

In this paper, we study generalized Douglas-Weyl $(\alpha, \beta)$-metrics. Suppose that an regular $(\alpha, \beta)$-metric $F$ is not of Randers type. We prove that $F$ is a generalized Douglas-Weyl metric with vanishing S-curvature if…

In this paper, we consider doubly warped product (DWP) Finsler manifolds with some non-Riemannian curvature properties. First, we study Berwald and isotropic mean Berwald DWP-Finsler manifolds. Then we prove that every proper Douglas…

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…

Finsler metrics with relatively non-negative (non-positive, respectively), constant and isotropic stretch curvatures are investigated in this paper. In particular, it is proved that every non-Riemannian $(\alpha, \beta)$-metric with a…

In this short paper, we study a symmetric covariant tensor in Finsler geometry, which is called the mean Berwald curvature. We first investigate the geometry of the fibres as the submanifolds of the tangent sphere bundle on a Finsler…

In this short paper, we prove that a Finsler manifold with vanishing Berwald scalar curvature has zero $\mathbf{E}$-curvature. As a consequence, Landsberg manifolds with vanishing Berwald scalar curvature are Berwald manifolds. This…

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 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 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…

The flag curvature of a Finsler metric is called a Riemannian quantity because it is an extension of sectional curvature in Riemannian geometry. In Finsler geometry, there are several non-Riemannian quantities such as the (mean) Cartan…

This paper gives new insights into the class of Generalized Douglas Weyl ($GDW$)-metrics. This projective invariant class of Finsler metrics, contains some well-known Finsler metrics such as Douglas, Weyl and $R$-quadratic metrics. Here,…

In this paper, we investigate the spherically symmetric Finsler metrics with isotropic S-curvature and obtain a characterized equation. As an application, we prove that these metrics with Douglas type must be Randers metrics or Berwald…

This paper presents a pioneering projective invariant in Finsler geometry, introducing a new class of Finsler metrics that are preserved under projective transformations. The newly formulated weakly generalized Douglas-Weyl $(W-G D W)$…

The flag curvature is a natural extension of the sectional curvature in Riemannian geometry, and the S-curvature is a non-Riemannian quantity which vanishes for Riemannian metrics. There are (incomplete) non-Riemannian Finsler metrics on an…