1) umbilic-free submanifold
紧致无脐点子流形
1.
Let M be an umbilic-free submanifold in unit sphere,we have calculated the Laplace of Blaschaketensor,when ‖A‖ satisfies certain conditions,we have given Moebius characterizations of these submanifolds.
设M为单位球中Moebius形式为零的紧致无脐点子流形,计算Blaschake张量A的平方的Laplace算子Δ‖A‖2,当‖A‖满足一定条件时,得到这类子流形的分类。
2) compact submanifolds
紧致子流形
1.
This paper deals with the compact submanifolds of constant mean curvature in space forms.
研究空间形式中常平均曲率的紧致子流形，建立了一个关于截曲率下界估计的不等式，通过计算和估计第二基本形式长度平方的Ｌａｐｌａｃｉａｎ，得到了关于数量曲率的一个邱成桐型积分不等
3) compact submanifold
紧致子流形
1.
The compact submanifolds in quasi constant curvature Riemannian manifolds with Parallel Mean Curature Vector were studied.
研究拟常曲率黎曼流形中具有平行平均曲率向量的紧致子流形。
2.
A compact submanifold in the local symmetry and complete Riemann manifold with parallel mean curvature vector field was studied, and a pinching theorem of the square of the length of the second fundamental form of this kind of submanifolds was given.
研究了局部对称完备黎曼流形中的具平行中曲率场的紧致子流形 ,得到这类子流形的第 2基本形式模长平方的一个拼挤定理 ,主要证明了当 Mn 是 Nn+p的紧可定向的子流形且具有平行中曲率向量时 ,∫M32 s2 + 83( 1 -δ) ( p -1 ) n -1 s+ ( 1 -2δ -λ| H | ) ns dv≥ 0 ,其中 λ表示 M的沿中曲率方向的第 2基本形式的最小特征值 。
4) Pseudo-umbilical Submanifold
伪脐点子流形
1.
Pseudo-umbilical Submanifolds in a Riemannian Manifold of Quasi Constant Curvature;
拟常曲率Riemann流形中的伪脐点子流形
5) totally-Umbilical
全脐点子流形
6) compact manifold without boundary
紧致无边流形
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