Abstract:

In this paper, we study Generalized Douglas-Weyl spray. We show that a spray $G$ is a Generalized Douglas-Weyl spray if and only if it is $W$-quadratic. As a corollary, we show that a Finsler metric $F$ is a Generalized Douglas-Weyl metric if and only if it is $W$-quadratic. Furthermore, we consider $R$-quadratic spray and prove that a spray $G$ is $R$-quadratic if and only if $\dot{B}^{~i}_{j~kl}=0$.

Key words: Spray, Weyl curvature, Douglas Tensor