曲率张量

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。

Firstly, we introduce the technology of seismic geometric attribute for fault identification detailedly at home and abroad. Secondly we study the coherence, texture,curvature attribute and tricolor display technology of RGB to identify fault; In the part of coherence,we compare the traditional algorithms with model and actual data,mainly study the geometric structural tensor and wavelet multi-scale sub-frequency coherent algorithm; In the part of texture attribute, we introduce texture energy, texture contrast, texture entropy and texture homogeneity attribute.By merging texture attributes of different directions,the effect are more clear; In the part of curvature attribute,we study and analyze fractional-order curvature attribute's extraction and its application in fault identification; The RGB display technology mainly introduces how to merge multi-attributes in order to getting more richer and more clearer information.

首先具体先容了地震几何属性识别断层技术的国内外研究现状；然后分别研究了相干属性、纹理属性、曲率属性和RGB三原色显示技术来识别断层；其中相干属性通过模型和实际资料对传统相干体算法进行了对比，重点研究了几何结构张量相干体算法和小波多标准分频相干体算法；纹理属性主要先容了纹理能量、纹理对比、纹理熵和纹理一致性属性，通过对不同方向的纹理属性进行融合，效果更清楚；曲率属性重点分析了分波数曲率属性提取及其在断层识别中的应用；RGB三原色显示技术则主要先容了如何进行多属性融合来或得更丰富、清楚的信息，在此基础上开发了基于。

The results show that structure curvature is negatively related to coalbed gas content,relative gas emission rate,outburst gas and coal amounts which reflect No15 coalbed of Ji is above the neutral plane of folds.That is,the No15 coalbed of Ji Group is compressed in incline and is tensed in anticline,and the higher structure curvature is,the higher stress is.

结果表明，构造曲率与瓦斯含量、瓦斯相对涌出量、突出瓦斯量、突出煤量呈负相关关系，反映研究区己15煤层位于褶皱中和面以上，即煤层在向斜轴部受挤压而背斜轴部受拉张，正曲率值反映煤层受到拉张应力作用，负曲率值反映煤层受到挤压应力作用，曲率绝对值越大，受力越大。

A method is proposed to calculate these features from a general quadric surface fitted at each point.

本文提出了一种从散乱坐标点拟合一般二次曲面，然后估计曲率张量的方法。

The space-like hypersurfaces with constant scalar curvature in a de Sitter space were studied and a pinching theorem on the square of the norm of the second fundamental form was obtained.

研究de Sitter空间中具有常数量曲率的类空超曲面，将Cheng-Yau的自共轨运算元口作用在对称张量T上，得到了这类超曲面关於第二基本形式模长平方的一个拼挤定理，加强了已有的相应结果。

Let x be an immersion of a compact Willmore surface M into the n-dimensional unit sphere Sn. In this thesis we first consider the Willmore surfaces in the unit 3-sphere, and establish an integral inequality for the square of the length of the trace free part of the second fundamental form and the mean curvature.

令x是一个从紧致威尔摩曲面M到n 维单位球面Sn的浸入，在本论文中我们首先考虑3维单位球面中的威尔摩曲面并建立一个包含第二基本型式迹为零部份的张量长度平方与平均曲率之积分不等式。

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。