ASSOCIATED CURVES OF A FRENET CURVE IN THE DUAL LORENTZIAN SPACE


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Abali B., YÜCESAN A.

COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, vol.71, no.1, pp.285-304, 2022 (Peer-Reviewed Journal) identifier

  • Publication Type: Article / Article
  • Volume: 71 Issue: 1
  • Publication Date: 2022
  • Doi Number: 10.31801/cfsuasmas.877170
  • Journal Name: COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS
  • Journal Indexes: Emerging Sources Citation Index, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.285-304
  • Keywords: Dual Lorentzian space, associated curves, dual general helix, dual slant helix, prin-cipal directed rectifying curve, SURFACES, HELICES

Abstract

In this work, we firstly introduce notions of principal directed curves and principal donor curves which are associated curves of a Frenet curve in the dual Lorentzian space D-1(3). We give some relations between the curvature and the torsion of a dual principal directed curve and the curvature and the torsion of a dual principal donor curve. We show that the dual principal directed curve of a dual general helix is a plane curve and obtain the equation of dual general helix by using position vector of plane curve. Then we show that the principal donor curve of a circle in D-2 or a hyperbola in D-1(2) and the principal directed curve of a slant helix in D-1(3) are a helix and general helix, respectively. We explain with an example for the second case. Finally, according to causal character of the principal donor curve of principal directed rectifying curve in D-1(3), we show this curve to correspond to any timelike or spacelike ruled surface in Minkowski 3-space R-1(3).