欧氏超曲面上的一类紧致梯度Ricci孤立子

A Class of Compact Gradient Ricci Solitons on Euclidean Hypersurfaces

本文将讨论欧氏空间中超曲面上的一类特殊Ricci孤立子,得到:若(M^n,g,ρ)为一个n维的Ricci孤立子,则在欧氏空间的紧致超曲面中不存在以位置向量函数模长平方的一半为梯度势函数,ρ=1的一类特殊的收缩梯度Ricci孤立子。

In this paper,we will discuss a class of special Ricci solitons on hypersurfaces in Euclidean space,and obtain that if(M^n,g,ρ)be a Ricci soliton on hypersurface,then there is no special shrinking gradient Ricci soliton on compact hypersurfaces in Euclidean space,where half of the square of the modulus length of the position vector function and ρ=1 is the gradient potential function.