三维Minkowski空间中的一类螺旋面
A Kind of Helicoidal Surface in 3-Dimensional Minkowski Space

作者: 吴 珩 , 黄平亮 :上海大学理学院数学系,上海;

关键词: Minkowski空间螺旋面平均曲率高斯曲率Minkowski Space Helicoidal Surface Meaning Curvature Gauss Curvature

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。

Abstract: 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).

文章引用: 吴 珩 , 黄平亮 (2015) 三维Minkowski空间中的一类螺旋面。 理论数学, 5, 136-142. doi: 10.12677/PM.2015.54021

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