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

YILDIRIM H., YÜCE S., KURUOĞLU N.

Acta Mathematica Scientia, cilt.31, sa.1, ss.172-180, 2011 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 31 Sayı: 1
  • Basım Tarihi: 2011
  • Doi Numarası: 10.1016/s0252-9602(11)60218-x
  • Dergi Adı: Acta Mathematica Scientia
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.172-180
  • Anahtar Kelimeler: Holditch Theorem, Lorentzian matrix multiplication, Lorentzian motion, Orthogonal projection area
  • İstanbul Gelişim Üniversitesi Adresli: Evet

Özet

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.