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

作　　者：周世武 汤建钢 杨成[2] 李体耀 Zhou Shiwu;Tang Jiangang;Yang Cheng;Li Tiyao(Yili Normal University,Yining,Xinjiang 835000,China;Civil Aviation Fight University of China,Guanghan,Sichuan 618307,China;Chongqing Normal University,Chongqing 400047,China)

机构地区：[1]伊犁师范大学,新疆伊宁835000 [2]中国民航飞行学院,四川广汉618307 [3]重庆师范大学,重庆400047

出　　处：《伊犁师范学院学报（自然科学版）》2019年第4期1-12,共12页Journal of Yili Normal University：Natural Science Edition

摘　　要：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.

关 键 词：齐次线性方程组及其基础解系 m维流形 m维超平面 m维流形的法向量 

分 类 号：O186.11[理学—数学]