In this paper we study the properties of special (α, β)-metric α α−β + β, the Randers change of Matsumoto metric. We find a necessary and sufficient condition for this metric to be of locally projectively flat and we prove the conditions for this metric to be of Berwald and Douglas type.

Divergences, also known as contrast functions, are distance-like quantities defined on manifolds of non-negative or probability measures and they arise in various theoretical and applied problems. Using ideas in optimal transport, we introduce and study a parameterized family of $L^{(\pm \alpha)}$-divergences which includes the Bregman divergence corresponding to the Euclidean quadratic cost, a...

Abstract In this paper, we study locally projectively flat Finsler metrics of constant flag curvature. We find equations that characterize these by warped product. Using the obtained equations, manufacture new product vanishing These contain metric introduced Berwald and spherically symmetric given Mo-Zhu.

Abstract In the present paper we examine a projectively flat spacetime solution of F ( R )-gravity theory. It is seen that once deploy projective flatness in geometry spacetime, matter field has constant energy density and isotropic pressure. We then make condition weaker discuss effects harmonic theory show this case reduces to generalised Robertson-Walker with shear, vorticity, acceleration f...

A ring R is called left GF-closed, if the class of all Gorenstein flat left Rmodules is closed under extensions. The class of left GF-closed rings includes strictly the one of right coherent rings and the one of rings of finite weak dimension. In this paper, we investigate the Gorenstein flat dimension over left GF-closed rings. Namely, we generalize the fact that the class of all Gorenstein fl...

From [4] we continue the algebraic investigation of generalized and equiaffine curvature tensors in a given pseudo-Euclidean vector space and study different orthogonal, irreducible decompositions in analogy to the known decomposition of algebraic curvature tensors. We apply the decomposition results to characterize geometric properties of Codazzi structures and relative hypersurfaces; particul...

In this paper we study spherically symmetric metrics on a space in $\mathbb{R}^n$ with scalar and constant flag curvature also obtain families of type metrics. Many explicit examples are provided for Douglas curvature. Furthermore, new projectively flat Finsler given. We provide family which not type.