查询词典 mean curvature

We then introduce a conformal invariant quantity which is formulated in terms of the square of the length of the trace free part of the second fundamental form and the mean curvature, and prove that if this quantity is bounded above by that value of the Clifford torus then x is either a totally umbilical sphereor a conformal Clifford torus.

接著我们介绍一个由第二基本型式迹为零部份的张量长度平方与平均曲率形成的保角不变量，并证明此保角不变量的上界若为Clifford环面之值，则x不是全脐球面就是Clifford环面的保角类。

Submanifold; Homology group; Topological sphere theorem; L~2 harmonic 1-forms; Ends; Eigenvalue; Mean curvature; Second fundamental form

基础科学，数学，几何、拓扑子流形；同调群；拓扑球面定理； L~2调和1-形式；端；特征值；平均曲率；第二基本形式

And obtain that compact submanifolds with parallel mean curvature vector must be totally geodesic.

以及具有平行平均曲率向量的紧致子流形的全测性质。

Some uniform formulae are established, which link the Laplacian of the position vector function to the mean curvature vector field on any submanifold in the space forms.

讨论空间型中的位置向量场，建立一组统一的公式，将子流形的平均曲率向量场与位置向量及其衍生函数的Laplacian联系在一起。

A pinching theorem of compact pseudoumbilical submanifolds with parallel mean curvature vector in a locally symmetric conformally flat Riemannian manifolds

研究了复空间形式中具有平行法平均曲率向量的紧致全实伪脐子流形。

This pepediscusses compact submanifoldsoftheunit sphere Study is made on conditions ofsubmanifolds with parallel mean curvature vector,submanifolds with flat normal bundle and pseudo-umbilical submanifolds to be umbilical respectively.

本文讨论球的紧致子流形，研究具平行平均曲率向量的，具平坦法丛的、以及伪脐子流形成为全脐子流形的条件，得到几个关于第二基本形式长度千方S的pinching条件。

The relations among three parallel sections,such as parallel mean curvature vector fields, parallel isoperimetric section and parallel umblic section,on submanifolds in the constantly curved Riemannian manifolds R ~ are studied.

讨论常曲率空间Rn+p中子流形上三类平行截面：平行平均曲率向量场、平行等参截面、平行脐截面三者之间的相互关系。

In this thesis, we note in particular the Alexandrov theorem, which is concerned with the constant mean curvature.

在本文中，我们给出了一个与平均曲率有关的Alexandrov定理的另一证明。

The mean curvature flow is a very important geometric evolution equation.

中曲率流是非常重要的几何发展方程。

In the present paper,a sharp inequality is obtained between the Ricci curvature and the squared mean curvature of semi-invariant submanifold s in cosymplectic space forms,and some conditions are reached to make the equality hold.

对余辛流形的半不变子流形进行研究，利用曲率的分量表示之间的简单的代数关系，得到了这类子流形的R icc i曲率与平均曲率平方之间的一个不等式，并讨论了等式成立的充分必要条件

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。