欧氏空间Rn+1中m维流形法向量的计算方法

The Method of Calculating the Normal Vector of m-Dimensional Manifold in Euclidean Space Rn+1

首先给出了齐次线性方程组(0.1)基础解系的表达式,即定理1.1、定理1.2,由此得到了欧氏空间Rn^+1中m维流形在点P的法向量系就是方程组(0.1)的基础解系,即定理2.1.当m=n时,则法向量唯一(设n1,n是两个法向量,若n1=λn,则称n1,n是一个法向量).当m<n时,则法向量不唯一.然后讨论了法向量的相关性质,性质1~性质6,以及某一类两个法向量的内积计算公式,即定理3.2,这也是某一类两个向量的内积公式.

First,given the expressions of the fundamental system of solutions of homogeneous linear equations(0.1),that the theory 1.1,1.2,the normal vector system of m-dimensional manifold at point P in Euclidean spaceRn^+1 is the basic solution system of the system of equations(0.1),that the theory 2.1.When m=n,then the normal vector is unique(letn1,n be two normal vectors,if n1=λn,then n1,n is a normal vector).When m<n,the normal vector is not unique.Then the related properties of normal vector are discussed,Property 1~property 6,and the inner product formula of two normal vectors of a certain class,that theorem 3.2,which is also the inner product formula of two vectors of a certain class.