Curvature Submanifolds With Mean Curvature Vector Parallel

What is the submanifold is an important research field of differential geometry.In this paper,we study subcurvatures with parallel mean curvature vector.The main conclusion is:Let Nn+P be a hypersurface in Euclidean space Rn+p+1,Mn is the parallel submanifold of the compact boundless average curvature vector in Nn+p.If the main curvature ? of Nn+p satisfied:c1?|?|?c2(c1,c2>0),then there is fM[(2-1/p)S2+n|H|S3/2-nc12S+c22n2H2}*1?0.Where S is the square of the mod-ule length of the second basic from of submanifold,and H is its average curvature.This is,we get a Simons type integral inequality.