‎In this paper we first obtain the non-Riemannian Randers metrics of Douglas type on two-step homogeneous nilmanifolds of dimension five‎. ‎Then we explicitly give the flag curvature formulae and the $S$-curvature formulae for the Randers metrics of Douglas type on these spaces‎. ‎Moreover‎, ‎we prove that the only simply connected five-dimensional two-step homogeneous Randers nilmanifolds of D...

in this paper, we study a class of finsler metrics which contains the class of p-reducible andgeneral relatively isotropic landsberg metrics, as special cases. we prove that on a compact finsler manifold,this class of metrics is nothing other than randers metrics. finally, we study this class of finsler metrics withscalar flag curvature and find a condition under which these metrics reduce to r...

In this paper we study lifted left invariant $(\alpha,\beta)$-metrics of Douglas type on tangent Lie groups. Let $G$ be a group equipped with $(\alpha,\beta)$-metric $F$, induced by Riemannian metric $g$. Using vertical and complete lifts, construct the $F^v$ $F^c$ $TG$ give necessary sufficient conditions for them to type. Then, flag curvature these metrics are studied. Finally, as some specia...

We study an important class of Finsler metrics — Randers metrics. We classify Randers metrics of scalar flag curvature whose S-curvatures are isotropic. This class of Randers metrics contains all projectively flat Randers metrics with isotropic S-curvature and Randers metrics of constant flag curvature.

In this essay, we study the sufficient and necessary conditions for a Randers metrc to be of constant Ricci curvature, without the restriction of strong convexity (regularity). A classification result for the case ‖β‖α > 1 is provided, which is similar to the famous Bao-Robles-Shen’s result for strongly convex Randers metrics (‖β‖α < 1). Based on some famous vacuum Einstein metrics in General R...

In this paper, we study generalized Douglas-Weyl Finsler metrics. We find some conditions under which the class of generalized Douglas-Weyl (&alpha, &beta)-metric with vanishing S-curvature reduce to the class of Berwald metrics.

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.

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.