摘要
设M是n+p维单位球面S^(n+p)的n维紧致子流形,n=2,3,4;M具有平行平均曲率向量,若M的第二基本形式长度的平方S≤(2/3)n处处成立,则M是全脐点的或Veronese曲面。
Let M be an n-dimensional compact submanifold with parallel mean curvature tensor in unit sphere s^(n+p) with dimension n-p.S be the square of the length of second fundamental form of M; if n =2,3,4. and S satisfies S≤(2/3)n everywhere on M, then M must be totally umbilical or Veronese surface.
基金
国家科学基金
关键词
子流形
单位球面
PINCHING定理
second fundamental form, mean curvature, totally umbilical submanifolds