1) Moebius submanifold
Moebius子流形
2) Moebius form
Moebius形式
1.
Four basic invariants of x under the Moebius transformation group in S~(n+1) are:a Riemannian metric g called Moebius metric,a 1-formΦcalled Moebius form,a symmetric (0,2) tensor A called Blaschke tensor and a symmetric (0,2) tensor B called Moebius second fundamental form.
设x:M~n→S~(n+1)是(n+1)-维单位球面上不含脐点的超曲面,在S~(n+1)的Moebius变换群下浸入x的四个基本不变量是:一个黎曼度量g称为Moebius度量;一个1-形式Φ称为Moebius形式;一个对称的(0,2)张量A称为Blaschke张量和一个对称的(0,2)张量B称为Moebius第二基本形式。
2.
This paper,proves the following main theorem:Let x:M→S n+1 be a hypersurface in S n+1 without umbilic point,n3,Q and K are respectively the infimum of Ricci curvature and normalized scalar curvature with respect to the Moebius Metric,if the Moebius form Φ is parallel and Q-K(n-2n) 2,then n is even and x is Moebius equavalent to the Clifford minimal torus :S n2 (12)×S n2 (12)→S n+1 .
设M是单位球面Sn+1无脐点超曲面,在Sn+1Moebius变换群下M的基本不变量是Moebius度量g,Moebius形式Φ,Moebius第二基本形式B和Blaschke张量A。
3.
In this paper, we prove the reduction of codinemsion for the surfaces in Sn with vanishing Moebius form and flat Moebius normal bundle, and classify this sort of surfaces.
本文证明了Sn中Moebius形式为零且法丛平坦的曲面的余维数约化定理,并且给出了这类曲面的分类。
3) Moebius second fundamental form
Moebius第二基本形式
1.
Four basic invariants of x under the Moebius transformation group in S~(n+1) are:a Riemannian metric g called Moebius metric,a 1-formΦcalled Moebius form,a symmetric (0,2) tensor A called Blaschke tensor and a symmetric (0,2) tensor B called Moebius second fundamental form.
设x:M~n→S~(n+1)是(n+1)-维单位球面上不含脐点的超曲面,在S~(n+1)的Moebius变换群下浸入x的四个基本不变量是:一个黎曼度量g称为Moebius度量;一个1-形式Φ称为Moebius形式;一个对称的(0,2)张量A称为Blaschke张量和一个对称的(0,2)张量B称为Moebius第二基本形式。
2.
Moebius second fundamental form is important Moebills invariable on the unit sphere of submanifolds,In this paper,we classify the surface in S~3 with semi—parallel Moebius second fundamental form.
Moebius第二基本形式是单位球面上子流形的重要的Moebius不变量,本文给出了S3中具有半平行Moebius第二基本形式的曲面的分类。
4) Egg shape submanifold
卵形子流形
5) submanifold
['sʌb'mænifəuld]
子流形
1.
Stable Integral Currents in Submanifolds Immersed in Euclidean Space;
欧氏空间的子流形中的稳定积分流
2.
Important theorem on submanifold in space form with paralled Ricci curvature;
常曲率空间中Ricci曲率平行的子流形的一个重要定理及应用
3.
Curvature and geometric property of submanifolds in Euclidean spaces;
欧氏空间中子流形的曲率与几何性质
6) submanifolds
子流形
1.
The Topology of Submanifolds in a Sphere S~(n+p)(c);
球面S~(n+p)(c)中子流形的拓扑(英文)
2.
A remark on projectively flat totally realminimal submanifolds in CP~n;
关于复射影空间射影平坦、全实极小子流形的注记
3.
Relations Between Focal Points and Shape Operators of Submanifolds in Non-Compact Symmetric Spaces;
非紧对称空间中子流形焦点和形算子间的关系
补充资料：子流形
见微分流形。
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条