On Some Inequalities for Submanifolds of Bochner-Kaehler Manifolds

Abstract

B. Y. Chen established sharp inequalities between certain Riemannian invariants and the squared norm of mean curvature for submanifolds in real space form as well as in complex space form. In this paper we generalize Chen inequalities for submanifolds of Bochner Kaehler manifolds. Moreover, we study CR-warped product submanifolds of Bochner Kaehler manifold and establish an inequality for scalar curvature.