四维欧氏空间中的向量积运算及其应用

On the Vector Product of Three Vectors in 4-Dimensional Euclidean Space and Its Application

本文引进四维欧氏空间中三个向量的向量积运算,并讨论这种运算的一些性质。作为应用,将三维欧氏空间中关于曲线的Frenet公式推广到四维欧氏空间,获得了四维欧氏空间中曲线的几个本征参数:曲率、挠率、第三曲率。

In this paper, we define the vector product of three vectors and then some funny properties are proved. Then, we construct the standard orthogonal basis at the normal point of curves and obtain the Frenet formulae for curves in 4 - dimensional Euclidean space. Three important parameters are introduced which are curvature, torsion and third curvature.