度量矩阵在微分几何中的运用

摘要

将微分几何中的主要内容曲面的第一基本型、第二基本型和活动标架统一用度量矩阵来处理，有效避开了与微分方程有关的一些问题，简化了曲面论中某些定理的证明。指出了一阶标架场的选择与度量矩阵的关系。%The main content of differential geometry that is surfaces first basic type,surfaces second basic type and moving frame,was unified with measure matrix to deal with.Effectively avoided some of the problems associated with differential equations,simplified the proof of certain theorems on the surface.Pointed out the relationship between the first-order selection frame field with metric matrix.