Sasakian anti-holomorphic submanifolds of a Kaehler manifold

Abstract

Let $ M$ be a connected Sasakian anti-holomorphic submanifold of a Kaehler mnifold with flat norml connection and with dim $ D\ge 4$, where $ D$ is the holomorphic distribution on $ M$. We show that $ M$ is locally Riemannian product $ M' \times M''$ where $ M'$ is homothetic to a Sasakian manifold and $ M''$ is a locally Euclidean space.