Chen-Ricci inequalities for submanifolds of Riemannian and Kaehlerian product manifolds

Abstract

Some examples of slant submanifolds of almost product Riemannian manifolds are presented. The existence of a useful orthonormal basis in proper slant submanifolds of a Riemannian product manifold is proved. The sectional curvature, the Ricci curvature and the scalar curvature of submanifolds of locally product manifolds of almost constant curvature are obtained. Chen Ricci inequalities involving the Ricci tensor and the squared mean curvature for submanifolds of locally product manifolds of almost constant curvature are established. Chen Ricci inequalities for different kinds of submanifolds of Kaehlerian product manifolds are also given.