Ideal Hypersurfacces In Euclidean Spaces Satisfying â–³(H|â†')=λ(H|â†')

Along with the research of biharmonlic submanifolds has become increasingly mature in Euclidean space,the study of ideal hypersurface is quite favorite of peo-ple.In this paper,for our ideal hypersurfaces in Euclidean space to do a thorough study.In the mean curvature vector field to satisfy the equation △H=λH(λa constant)condition,which is a natural generalization of the biharmonic submani-fold equation △H=0,we show that mean curvature is a constant of δ(2)-ideal hypersurfaces and δ(3)-ideal hypersurfaces in Euclidean sphere En+1.This paper is divided into the following three sections:In Section one,we mainly recall some basic concepts,basic formulas,and the definition of ideal with δ-invariants.In Section two,we investigate the δ(2)-ideal hypersurfaces of Euclidean sphere En+1 satisfying ΔH=λH(λ a constant),and prove the mean curvature is a constant(see Theorems 2.1).In Section three,we investigate the δ(3)-ideal hypersurfaces of Euclidean sphere En+1 satisfying △H=λH(λa constant),and prove the mean curvature is a constant(see Theorem 3.1).