Ricci curvature of integral submanifolds of an $f.p.k.$-space form

Abstract

In this paper, relationships between the Ricci curvature and the squared mean curvature for integral submanifolds of an $f.p.k.$-space form by a basic inequality, are studied. We show that if an integral submanifold of maximum dimension of an $f.p.k.$-space form satisfies the equality case, then it must be minimal.