第二基本形式

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

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。

Therefore, it is imperative that you need to be prepared for the great change that is about to occur.

所以，你需要为快要出现的伟大改变准备好，这是必要的。

If u agree with our suggestion of dicker trade,we will exchange paper with u wood.

如果你方同意我们进行易货贸易的建议，我们将用纸与你们交换木材。