A Condition for a Sasakian Manifold to Be of Constant Curvature

In this paper we give a generalization of some results due to T. Takahashi [5] and M. Okumura [4]. Explicitly, we study an equation of theform R(X,Y)A=0 where X,Y are arbitrary vector fields on a Sasakian manifold and A a (1,3)-tensor field which generalizes the Riemann curvaturetensor, Weyl conformal curvature tensor, Weyl projective curvature tensor and Yano concircular curvature tensor. The result which we obtain saysthat in complementary conditions the manifold is of constant curvature.