东北大学学报（自然科学版）

东北大学学报(自然科学版) ›› 2009, Vol. 30 ›› Issue (2): 302-304.DOI: -

• 论著 • 上一篇    

三维Minkowski空间中的平移曲面

袁媛;张金亮;李春秀;刘会立;   

  1. 东北大学理学院;
  • 收稿日期:2013-06-22 修回日期:2013-06-22 出版日期:2009-02-15 发布日期:2013-06-22
  • 通讯作者: Yuan, Y.
  • 作者简介:-
  • 基金资助:
    国家自然科学基金资助项目(10371013)

Translation surfaces in 3-D Minkowski space

Yuan, Yuan (1); Zhang, Jin-Liang (1); Li, Chun-Xiu (1); Liu, Hui-Li (1)   

  1. (1) School of Sciences, Northeastern University, Shenyang 110004, China
  • Received:2013-06-22 Revised:2013-06-22 Online:2009-02-15 Published:2013-06-22
  • Contact: Yuan, Y.
  • About author:-
  • Supported by:
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摘要： 在三维Minkowski空间中,存在类空、类时和类光三种向量,选取这三种向量中的任意两种作为两个平移方向,可以将平移曲面分为六类.在伪正交标架下,选取一种新的度量形式,对沿两个类光方向平移的平移Weingarten曲面进行了研究.首先,根据微分几何中的基本知识,得到了该种度量形式下的平移曲面的第一、第二基本形式以及高斯曲率和平均曲率;然后,主要利用高斯曲率和平均曲率之间的线性关系和平方关系,得到了这类平移曲面的分类定理.

关键词: Minkowski空间, 平移曲面, Weingarten曲面, 伪正交标架

Abstract: There are three kinds of vectors in the 3-D Minkowski space, i.e., space-like, time-like and light-like vectors among which choosing any two vectors as the directions of translation will divide the translation surfaces into six types. A new metric form is chosen to study the Weingarten translation surfaces which are translating in the two null directions in a pseudo-orthogonal frame. Then, the first and second fundamental forms, Gaussian curvature and mean curvature of the surfaces are directly calculated according to the principles of differential geometry. It follows that some theorems of classification of those translation surfaces are given mainly by virtue of the linear and square relationships between the Gaussian curvature and the mean curvature.

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