三维Minkowski空间中的一类螺旋面

摘要

三维Minkowski空间中，螺旋面由一条平面曲线进行螺旋运动生成。本文研究以类光向量为轴进行螺旋运动所生成的螺旋面，主要讨论平均曲率H和高斯曲率K满足关系式a₁H2 + a₂K = g(s)的螺旋面的存在性以及表达式。A helicoidal surface in Minkowski 3-sapce is defined as the orbit of a plane curve under a screw motion. In this paper, we study a kind of helicoidal surface with light-like axis in Minkowski 3-space. As a result, we constructed the representation formulas for these helicoidal surfaces with meaning curvature H and Guass curvature K satisfying a₁H2 + a₂K = g(s).