In this paper, we study a special class of generalized Douglas-Weyl metrics whose Douglas curvature is constant along any Finslerian geodesic. We prove that for every Landsberg metric in this class of Finsler metrics, ? = 0 if and only if H = 0. Then we show that every Finsler metric of non-zero isotropic flag curvature in this class of metrics is a Riemannian if and only if ? = 0.

We study a special class of Finsler metrics which we refer to as Almost Rational (shortly, AR-Finsler metrics). give necessary and sufficient conditions for an manifold (M, F) be Riemannian. The rationality some geometric objects such Cartan torsion, geodesic spray, Landsberg curvature S-curvature is investigated. For particular subfamily have proved that if F has isotropic S-curvature, then th...

In this paper, we study the class of cubic (\alpha, \beta)-metrics. We show that every weakly Landsberg \beta)-metric has vanishing S-curvature. Using it, prove is a metric if and only it Berwald metric. This yields an extension Matsumoto's result for

in this paper, we study a special class of generalized douglas-weyl metrics whose douglas curvature is constant along any finslerian geodesic. we prove that for every landsberg metric in this class of finsler metrics, ? = 0 if and only if h = 0. then we show that every finsler metric of non-zero isotropic flag curvature in this class of metrics is a riemannian if and only if ? = 0.

Equality of hh -curvatures of the Berwald and Cartan connections leads to a new class of Finsler metrics, socalled BC-generalized Landsberg metrics. Here, we prove that every BC-generalized Landsberg metric of scalar flag curvature with dimension greater than two is of constant flag curvature.

In the present paper, we shall prove new characterizations of Berwald spaces and Landsberg spaces. The main idea inthis research is the use of the so-called average Riemannian metric.

In this paper, we study the curvature features of class homogeneous Randers metrics. For these metrics, first find a reduction criterion to be Berwald metric based on mild restriction their Ricci tensors. Then, prove that every with relatively isotropic (or weak) Landsberg must Riemannian. This provides an extension well-known Deng-Hu theorem proves same result for Berwald-Randers non-zero flag...

We study the new warped metric proposed by P. Marcal and Z. Shen. obtain differential equation of such metrics with vanishing Douglas curvature. By solving this equation, we all product metrics. show that Landsberg Berwald are equivalent. classify Ricci-flat Examples included.