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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.

It is still a long-standing open problem in Finsler geometry, there any regular Landsberg metric which not Berwaldian. However, are non-regular metrics The known examples established by G. S. Asanov and Z. Shen. In this paper, we use the Maple program to study some explicit of non-Berwaldian metrics. fact, such kinds very tedious complicated investigate. Nonetheless, packages simplify calculati...

In this paper we investigate the following question: under what conditions can a second-order homogeneous ordinary differential equation (spray) be the geodesic equation of a Finsler space. We show that the EulerLagrange partial differential system on the energy function can be reduced to a first order system on this same function. In this way we are able to give effective necessary and suffici...

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.