1) pseudo-spherical submanifold
伪球面子流形
1.
Decomposing the position vectors of a submanifold into the tangential and normal components,the present paper studies the conditions under which a compact space-like submanifold of pseudo-Euclidean space is pseudo-spherical submanifold.
将子流形的位置向量分解成水平分量和垂直分量,运用活动标架法研究伪欧氏空间的伪球面子流形。
2) pseudospherical surface
伪球形曲面
3) 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。
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) Pseudoumbilical submanifold
伪脐子流形
1.
Let N~n+p(c) be an (n+p)-dimensional Riemannian manifold with constant curvature c and M an n-dimensional compact pseudoumbilical submanifold of N~n+p(c).
讨论了常曲率黎曼流形Nn+p(c)中,具有平行平均曲率向量场的紧致伪脐子流形Mn的第二基本形式的Pinching问题,得到了Simons型不等式(定理2)和丘成桐型不等式(定理1)。
补充资料：伪球面
伪球面
pseudo-sphere
伪球面[冲践日。一刻犯比;nce哪c加pa」 曳物线(七刁d幻x)(x一“一切曲“，y=seChu)绕其渐近线(y=0，见图)旋转所构成的常负曲率曲面. 创卜 在半测地坐标(semi~g以)此ic姗11tina比)中线素有形式: d扩=d。2十氓h，竺d。，，“=常数 a(直线。二O是一测地线);而在等温坐标(is。山e爪以】coordinates)中有形式:、，2_。:兰兰止卫止，，_。， y-每个常负曲率曲面可局部嵌人于伪球面.伪球面的内蕴几何学局部地与双曲几何学一致(见Bdt.田11解释(价h以而泊忱rPre以ion)).
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参考词条