On generalized Douglas-Weyl spaces

In this paper, we show that the class of R-quadratic Finsler spaces is a proper subset of the class of generalized Douglas-Weyl spaces. Then we prove that all generalized Douglas-Weyl spaces with vanishing Landsberg curvature have vanishing the non-Riemannian quantityH, generalizing result previously only known in the case of R-quadratic metric. Also, this yields an extension of well-known Numata’s Theorem.