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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）

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【Author】 WU ai-ju JI yong-qiang (The mathematical and computer academy of Ningxia University,NingXia YinChuan 750021 Chian)

【机构】宁夏大学数学与计算机学院；宁夏大学数学与计算机学院宁夏银川 750021；宁夏银川 750021；

【摘要】设Mⁿ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）H²],则Mⁿ是S^n+p（c）中全脐子流形。再有Mⁿ关于平均曲率方向是全脐的,即Mⁿ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Mⁿ是S^n+p（c）中全脐子流形的三个平行定理。更多还原

【Abstract】 Let M" be a compact submanifold with positive curvature in the constant curvedmanifolds of Sn+p(c) ,(p - 1) + (4p - 6)H2]then M"be a totally umbilical submanifoldon 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) .更多还原