On complex Sasakian manifolds

In this article, we study a class of normal complex contact metric manifold called a complex Sasakian manifolds. This kind of manifolds have a globally defined complex contact form and normal complex contact structure. We define a complex Sasakian manifold by considering the real case and we present general properties. Also, we obtain some useful curvature relations. Finally, we examine flatness conditions for general curvature tensor B.