1) Moebius equivalent
Moebius等价
2) Moebius transformation
Moebius变换
1.
At last,a uniform spherical parameterization is generated by a Moebius transformation.
通过立体投影将现有的平面参数化方法推广到球面上,得到一个初始的球面参数化;为了减小变形,引入质心坐标进行全局优化;最后用Moebius变换均匀化最终的球面网格。
3) Moebius metric
Moebius度量
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。
4) 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。
5) Moebius invariant
Moebius不变量
1.
In this paper we investigate the conformal Gauss map of submanifolds in sphere space and get, by Moebius invariants, the condition for this kind of map to be harmonic.
本文研究球空间中子流形的共形高斯映射,用Moebius不变量刻划了该映射 为调和映射的条件。
6) Moebius minimal
Moebius极小
1.
In this paper,We prove the following theorem:Let α:M→S~3 be an umbilic-free surface in S~3,then α:M→S~3 is minimal if and only if x is Moebius minimal surface with constant mean Curvature.
本文给单位球面上的子流形为Moebius极小子流形的一个充要条件,并证明了S3中不含脐点的曲面为极小曲面当且仅当它为常平均曲率的Moebius极小。
补充资料：Moebius序列征
Moebius序列征
Moebius序列征只是一种表征，不是特异的，曾报道少数病例呈常染色体显性遗传的各种变异性表现。最基本的特征是面具样脸和第Ⅵ与第Ⅶ对颅神经麻痹。据尸解发现有四种方式的病理发育：①中脑核发育低下或缺如；②中脑核破坏性退变；③累及周围末梢神经；④一种肌病。表现：小颌是常见的特征。广泛累及颅神经，舌活动受限，和/或舌小。上睑下垂，和或突出的耳郭。1/3患者有马蹄内翻足。15%的患者有智力低下。面部无表情和口吃等。
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