Problem Of Pinching Of The Length Of Ricci Curvature Of The Minimal Submanifold In Space Form

Let f:Mn→Mn+pp(c) be an isometric of a Riemannian manifold into a Riemannian manifold with constant curvature. In this paper , we obtain a new Simons' type integral inequality by calculating the laplace of the square of the length of the Ricci curvature and obtain some interesting results from the Simon's type integral inequality. These results have relation to parallel Ricci curvature, so we consider the submanifold with parallel Ricci curvature and obtain an important identity. We have the class of minimal hypersurfaces of space with constant curvature by using the identity and generalize the results which have been known.