数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (1): 172-180.doi: 10.1016/S0252-9602(11)60218-X

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HOLDITCH THEOREM FOR THE CLOSED SPACE CURVES IN LORENTZIAN 3-SPACE

 Handan Yildirim, Salim Y¨uce, Nuri Kuruoglu   

  1. Department of Mathematics, Faculty of Science, \.{I}stanbul University, Vezneciler, 34134, \.{I}stanbul, Turkey|Department of Mathematics, Faculty of Arts and Science, Y{\i}ld{\i}z Technical University, Esenler, 34210, \.{I}stanbul, Turkey|Department of Mathematics and Computer Sciences, Bah\c{c}e\c{s}ehir University, Faculty of Arts and Science, Be{\c s}ikta{\c s}, 34100, \.{I}stanbul, Turkey
  • 收稿日期:2008-02-26 修回日期:2008-10-20 出版日期:2011-01-20 发布日期:2011-01-20

HOLDITCH THEOREM FOR THE CLOSED SPACE CURVES IN LORENTZIAN 3-SPACE

 Handan Yildirim, Salim Y¨uce, Nuri Kuruoglu   

  1. Department of Mathematics, Faculty of Science, \.{I}stanbul University, Vezneciler, 34134, \.{I}stanbul, Turkey
  • Received:2008-02-26 Revised:2008-10-20 Online:2011-01-20 Published:2011-01-20

摘要:

In this article, we give the area formula of the closed projection curve of a closed space curve in Lorentzian 3-space L3. For the 1-parameter closed Lorentzian space motion in L3, we obtain a Holditch Theorem taking into account the Lorentzian matrix multiplication for the closed space curves by using their othogonal projections onto the Euclidean plane in the fixed Lorentzian space. Moreover, we generalize this Holditch Theorem for noncollinear three fixed points of the moving Lorentzian space and any other fixed point on the plane which is determined by these three fixed points.

关键词: Lorentzian matrix multiplication, Lorentzian motion, Holditch Theorem, orthogonal projection area

Abstract:

In this article, we give the area formula of the closed projection curve of a closed space curve in Lorentzian 3-space L3. For the 1-parameter closed Lorentzian space motion in L3, we obtain a Holditch Theorem taking into account the Lorentzian matrix multiplication for the closed space curves by using their othogonal projections onto the Euclidean plane in the fixed Lorentzian space. Moreover, we generalize this Holditch Theorem for noncollinear three fixed points of the moving Lorentzian space and any other fixed point on the plane which is determined by these three fixed points.

Key words: Lorentzian matrix multiplication, Lorentzian motion, Holditch Theorem, orthogonal projection area

中图分类号: 

  • 53A17