查询词典 fundamental form

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。

If we give some restrician to the intrinsic quantities of submanifolds, such as second fundamental form, scalar curvature,Ricci curvature or sectional curvature,then we can get some new property of the submanifolds.The procedure is called pinching problem of submanifolds.

对子流形的第二基本形式模长平方s，数量曲率R，Ricci曲率R_及截面曲率R_等内在量，加以某种限制，从而得到子流形的某些性质，叫做子流形的pinching问题。

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

Properties of Curves, Surface in Three Dimensions, The First Fundamental Form

课程内容：平面与空间中曲线，曲率和挠率，全曲率，同周边不等式，曲面的基本式，平

Then use this moving frame to compute the coefficients of the first fundamental form E, F, G and the coefficients of the second fundamental form L, M, N.

利用这个标架，计算曲面S的第一基本形式的系数E，F，G和第二基本形式的系数L，M，N。

More specifically, Gauss studied the geometry of surfaces based on the first fundamental form (also called "line element") of surfaces and generalized Euclidean geometry to "curved geometry" on surfaces.

局部微分几何的一个里程碑是 Gauss关于曲面的理论，他建立了基于曲面第一基本形式的几何，并把欧几里得几何推广到曲面上"弯曲"的几何。

Let x: M→S(superscript n+1)(n≥3) be a hypersurface in the (n+1)-dimensional unit sphere without umbilic points. Denote the Mbius metric, the Mbius form, the Blaschke form and the Mbius second fundamental form of x by G,Ф, A and B, repcectively, which are Mbius invariants in Mbius differential geometry.

设x： M→S(上标 n+1)(n≥3)是n+1-维单位球中的无脐点超曲面，Mbius不变量G，Ф，A和B分别表示x的Mbius度量，Mbius形式，Blaschke形式和Mbius第二基本形式。

In this article,we mainly study the space-like submanifolds with parallel mean curva-ture vector,constant scalar curvature or constant square length of the second fundamental form,respectively.We obtain some pinching theorems and rigidity results by estimating Laplace of the square length of the second fundamental form of the such submanifolds and using yaus maximum principle or Stokes Theorem.

本论文主要研究de Sitter空间中具有平行平均曲率向量、常数量曲率或第二基本形式模长平方是常数的三类类空子流形，并通过分别估计三种情形下子流形的第二基本形式模长平方的Laplace，利用Yau的极大值原理和Stokes定理，获得了这些子流形的一些拼挤定理和刚性定理。

Using the mathematical tool"DifferenceGeometry",it is possible to define the discrete geometric metrics such as discretefirst fundamental form,discrete second fundamental form,discrete unit mainnormal vector,discrete Gauss curvature,discrete mean curvature and discreteLaplacian.

首先，运用"差分几何"这一工具，可以构造离散第一、第二基本形式，离散单位主法向，离散高斯曲率，离散中曲率等离散几何量和离散Laplace算子。

Considering thought has its inherent characteristic (I, e, self-organization, freedom, fiction). The fundamental thought activity can be divided into perceptional, imaginal, abstract, illusional, renew, associational and inspirational and so on. All these analyse each fundamental form related to thought unit ("model"and"shape") as well as relationship between each different fundamental forms.

在该方针的指导下，在知识获取过程中提出&双向信息挖掘法&，通过目标分解和证据驱动两个过程，促动知识信息之间连接关系的变化，使领域专家能够全方位、多角度地认识这些信息对研究目标的贡献，便于发现一些隐蔽的或深层次的知识信息，促进内涵静态知识向内涵动态知识的完全转化。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。