四维Minkowski空间中伪零曲线的伴随曲线

Associate curve of pseudo null curve in 4-dimensional Minkowski space

定义了四维Minkowski空间中伪零曲线的伴随曲线.利用伪零曲线的特殊性,将欧氏空间中曲线的性质扩展到伪欧氏空间.通过对伪零曲线及其伴随曲线的Frenet标架的讨论,给出不同类型伴随曲线的曲率函数表达方式.讨论了特殊曲线的伴随曲线的曲率函数,并给出相应实例.

The associate curve of the pseudo null curve in 4-dimensional Minkowski space was defined.The properties of curves in Euclidean space are extended to pseudo-Euclidean space by using the particularity of pseudo null curve.By discussing the Frenet frame of the pseudo null curve and its associate curves,the expression of curvature functions of different types of associate curves were given.The curvature function of the associate curve of a special curve is discussed,and some examples were given.