RICCI CURVATURE OF SUBMANIFOLDS OF A SASAKIAN SPACE FORM

Abstract

Involving the Ricci curvature and the squared mean curvature, we obtain basic inequalities for different kind of submaniforlds of a Sasakian space form tangent to the structure vector field of the ambient manifold. Contrary to already known results, we find a different necessary and sufficient condition for the equality for Ricci curvature of C-totally real submanifolds of a Sasakian space form, and (2) of the fact that if a C-totally real submanifold of maximum dimension satisfies the equality case, then it must be must be minimal. Two basic inequalities for submanifolds of any Riemannian manofild, one involving scaler curvature and the squared mean curvature and the other involving the invariant and the squared mean curvature are also obtained. These results are applied to get corresponding results for submanifolds of Sasakian space forms.