on generalized berwald r-quadratic metrics

‎every riemannian metric is r-quadratic, while many finsler metrics have not this property‎. ‎a finsler metric is called r-quadratic if its riemannian curvature is quadratic in all direction at any points of the underlying manifold‎. ‎a finsler metric on a manifold is called a generalized berwald metric if there exists a covariant derivative such that the parallel translations induced by it preserve the finsler function‎. ‎in this paper‎, ‎we study the class of generalized berwald (α, β)-manifolds with r-quadratic properties and prove a rigidity result‎. ‎we show that such manifolds satisfy s=0 if and only if b=0‎.