Holditch theorem for the closed space curves in Lorentzian 3-space

YILDIRIM H., YÜCE S., KURUOĞLU N.

Acta Mathematica Scientia, vol.31, no.1, pp.172-180, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 31 Issue: 1
  • Publication Date: 2011
  • Doi Number: 10.1016/s0252-9602(11)60218-x
  • Journal Name: Acta Mathematica Scientia
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.172-180
  • Keywords: Holditch Theorem, Lorentzian matrix multiplication, Lorentzian motion, Orthogonal projection area
  • Istanbul Gelisim University Affiliated: Yes

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. © 2011 Wuhan Institute of Physics and Mathematics.