常曲率空间S^(n+p)(C)中具有平行中曲率向量的紧致伪脐子流形  

The Compact Pseudo - Umbilical Submanifold With Pallaedmean Curvature In The Constant Curved Manifold S^(n+p)(c)

作　　者：武爱菊[1] 纪永强[1] 

机构地区：[1]宁夏大学数学与计算机学院,宁夏银川750021

出　　处：《固原师专学报》2003年第3期10-13,共4页Journal of Guyuan Teachers College

摘　　要：设M^n是S^(n+p)(c)中具有平行中曲率向量的紧致正曲率子流形(p>1),当σ≤n/3p-5[(p-1)c+(4p-5)H^2],则M^n是S^(n+p)(c)中全脐子流形。再有M^n关于平均曲率方向是全脐的,即M^n是S^(n+p)(c)中伪脐子流形,将此定理条件减弱为紧致伪脐子流形,从而得到M^n是S^(n+p)(c)中全脐子流形的三个平行定理。Let M' be a compact submanifold with positive curvature in the constant curved manifolds of Sn+p(c) ,(p - 1) + (4p - 6)H2]then M'be a totally umbilical submanifold on the mean curvature vector direction.This paper weaken the conditions of the theorems,and obtained three pinching theorems. Then Mn be a totally umbilical submanifold of Sn+p(c) .

关 键 词：全脐子流形 伪脐子流形 子流形 

分 类 号：O186.1[理学—数学]