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

Pure Mathematics
Vol.05 No.04(2015), Article ID:15620,6 pages
10.12677/PM.2015.54021

A Kind of Helicoidal Surface in 3-Dimensional Minkowski Space

Heng Wu, Pingliang Huang

Department of Mathematics, College of Sciences, Shanghai University, Shanghai

Email: wlavande@shu.edu.cn

Received: Jun. 19th, 2015; accepted: Jul. 2nd, 2015; published: Jul. 8th, 2015

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).

Keywords:Minkowski Space, Helicoidal Surface, Meaning Curvature, Gauss Curvature

Email: wlavande@shu.edu.cn

1. 引言

(1.1)

1)若，则螺旋面的表达式为

2) 若，则螺旋面的表达式为

2. 背景知识

1)，则称是类空向量；

2)，则称是类时向量；

3)，则称是类光向量。

1)称为曲面的第一基本形式，其中称为第一基本量；

2)称为曲面的第二基本形式，其中称为第二基本量。

3. 主要结论的证明

(3.1)

1) 若时，有

(3.2)

，则(3.2)等价于

2) 若，即

(3.3)

(b为待定系数)为(3.3)式的解，将带入(3.3)式有

A Kind of Helicoidal Surface in 3-Dimensional Minkowski Space. 理论数学,04,136-142. doi: 10.12677/PM.2015.54021

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