2) pseudo-umbilical submanifold
伪脐子流形
1.
Two Pinching theorems for pseudo-umbilical submanifolds;
伪脐子流形的两个Pinching定理
2.
Researches the submanifolds in nested space,for constant curvature Riemannian submanifold in quasi-constant curvature manifold and pseudo-umbilical submanifold with parallel mean curvature vector in constant curvature Riemannian submanifold,presents three sufficient conditions for this pseudo-umbilical submanifold to be total-umibilical submanifold,generalizes the result of JI Yongqiang.
对于拟常曲率流形中的常曲率黎曼子流形以及常曲率黎曼子流形中具有平行中曲率向量的紧致伪脐子流形,给出了这种伪脐子流形是全脐子流形的3个充分条件,推广了纪永强的相关结果。
3.
For constant submanifolds in locally symmetric space,and pseudo-umbilical submanifold with parallel mean curvature vector in constant space,two sufficient conditions are given for pseudo-umbilical submanifold to be a totally umbilical submanifold in constant space.
研究了2个嵌套空间中子流形,对于局部对称空间中的常曲率黎曼子流形以及常曲率黎曼子流形中具有平行平均曲率向量的紧致伪脐子流形,给出了这种伪脐子流形是全脐子流形的两个充分条件。
3) totally umbilical submanifolds
全脐子流形
1.
In this paper, some properties of totally real and totally umbilical submanifolds of a complex projective space are obtained.
获得了复射影空间中全实全脐子流形的若干性质,并且证明了复射影空间中具有平行平均曲率向量的正曲率紧致全实子流形必是伪脐的。
2.
Some pinching theorems about totally real pseudo-umbilical submanifolds with parallel mean curvature vector becoming totallyreal and totally umbilical submanifolds are obtained by choosing a suitableframe ?eld.
通过选取合适的活动标架，获得具有平行平均曲率向量的全实伪脐子流形成为全实全脐子流形的若干Pinching定理。
4) pseudo-umbilical submanifolds
伪脐子流形
1.
The complete pseudo-umbilical submanifolds with parallel mean curvature vector in constant curvature space;
常曲率空间中具有平行平均曲率的完备伪脐子流形
2.
In this paper,the pseudo-umbilical submanifolds with parallel mean curvature vector in pseudo-Riemannian manifold is discussed.
研究了伪黎曼流形中具有平行平均曲率向量的伪脐子流形,Npn+p为n+p维完备连通伪黎曼流形,它的截面曲率KN满足a≤KN≤b,Mn为Npn+p中紧致的具有平行平均曲率向量的伪脐子流形。
3.
Let be a compact pseudo-umbilical submanifolds with parallel mean curvature vector in the quasi constant curvature space.
设Mn是拟常曲率空间Nn+p中具有平行平均曲率向量的紧致伪脐子流形,论证得到了这种子流形的两个内蕴积分不等式,从而给出了Mn是全脐子流形的两个内蕴充分条件。
5) Pseudoumbilical submanifolds
伪脐子流形
1.
In the first part, we consider the compact totally real pseudoumbilical submanifolds Mn that have nonzero parallel normalized mean curvature vector in complex space forms M(n+p)(c).
(1)讨论了复空间形式(?)~(n+p)((?))中具有非零平行法平均曲率向量的紧致全实伪脐子流形M~n，得到了(ⅰ)如果M~n在其点x的截面曲率的下确界函数K(x)满足条件：则M~n是全脐的。
6) totally umbilical submanifold
全脐子流形
1.
A totally umbilical submanifold of constant curvature space;
常曲率空间中的全脐子流形
2.
For constant submanifolds in quasi-constant curvature Riemannian manifold,and pseudo-umbilical submanifold with parallel mean curvature vector in constant space,three sufficient conditions are given for pseudo-umbilical submanifold to be a totally umbilical submanifold in constant space.
对于拟常曲率流形中的常曲率黎曼子流形以及常曲率黎曼子流形中的具有平行平均曲率向量的紧致伪脐子流形,给出了这种伪脐子流形是全脐子流形的3个充分条件。
3.
Let M2n+p+q1 be a (n+p+q)-dimensional δ-Pinching Riemannian manifold,M1n+p(c1) be a (n+p)-dimensional with constant curvature c1 in M2n+p+q,let M "be a compact pseudo-umbilical submanifold with parallel mean curvature vector in Mn+p(c1),we give some sufficient conditions that M "be a totally umbilical submanifold in M1n+p(c1).
设M2n+p+q是其截面曲率KM2ABAB满足O<δ脐子流形,给出Mn是M1n+p(c1)的全脐子流形的几个充分条件。
补充资料：伪流形
伪流形
伪流形l】娜习l〕J.‘翻d;nce聊MHoroo6p。”e]，n维的和闭的(或带边缘的) 一个具有下列性质的有限单纯复形(slrnPlicialco-mplex): a)它是无分支的(non~branching):每个(n一1)维单形恰好是二个(分别是一个或两个)n维单形的面;b)’它是强连通的(s加ngiy collneCted):任何两个，，维单形可用凡维单形的一个’‘链”连接起来.在该“链”中、每一对相邻的单形有一个公共的(n一1)维面; c)它有维数的齐性(山叱nsional homogeneity):姆一个单形是某个n维单形的一个面. 如果一个拓扑空问的某个三角剖分(triangu】ation)是伪流形，那么，它的任何一个三角剖分是伪流形.因此，人们可以论及拓扑空间是(或不是)伪流形的性质. 伪流形的例子:可三角剖分的Z上的紧连通同调流形(11Omology Tnanjfold);复代数簇(甚至有奇点的)及可三角剖分的紧流形上的向量丛的刃，扣1空间(Thom sPacc).直观地，一个伪流形可以当作一个具有奇点的流形的一般思想的组合实现，后者组成一个余维数2的集合.可定!砂性、定向和映射的度的概念对伪流形有意义，然而，在组合方法范围内，伪流形形成了这些概念的自然定义域(尤其形式上伪流形的定义比组合流形的定义更简单).流形中的一个闭链在某种意义下可以通过伪流形来实现(见Stee11r(〕d问题(Steenrod prob】em)).
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