Submanifolds With Parallel Mean Curvature Vector In Sphere

This article discusses Mn, the submanifold with parallel mean curvature vector in sphere Sn+p. By moving frame method and Hopf maximum principle, we get a pinching theorem which states that Mn lies in a totally geodesic 5n+1.This article consists of four chapters, the first chapter is the introduction of the research status of pinching problem in Riemannian manifold,the second chapter is the preliminaries, which introduces the Cartan lemma, the basic definitions and the formulas of Riemannian manifolds and Riemannian submanifolds, the third chapter is the Hopf maximum principle and the Simons inequality, the fourth chapter is the main part of this paper, the introduction and proof of our theorem obtained in this paper.