三维Minkowski空间中的类光螺线

摘要

Lightlike helices in 3D Minkowski space are studied.First,the Frenet frame of lightlike curves in 3D Minkowski space is given and the method of describing lightlike curves with lightlike curvature functions is proposed.Then,the lightlike helix definitions are given,which are classified as general lightlike helix, first slant lightlike helix and second slant lightlike helix according to that the inner product is a constant between the tangent vector,principal normal vector,binormal vector of a lightlike curve and a fixed direction vector,respectively.Finally,the characterizations of lightlike curvature functions of lightlike helices are studied and their specific expression forms in different conditions are obtained.%在三维Minkowski空间中讨论类光螺线.首先给出三维Minkowski空间中类光曲线的Frenet标架,提出用类光曲率函数来描述类光曲线的方法;其次给出类光螺线的定义,分别根据类光曲线的切向量、主法向量、副法向量与固定方向向量的内积为常数,将类光螺线分为一般类光螺线、第一类斜类光螺线和第二类斜类光螺线;最后研究三种类光螺线的类光曲率函数所具有的性质,并得到了各种情况下类光螺线的具体表达形式.