ASSOCIATED CURVES OF A FRENET CURVE IN THE DUAL LORENTZIAN SPACE
COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, cilt.71, sa.1, ss.285-304, 2022 (ESCI, TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 71 Sayı: 1
- Basım Tarihi: 2022
- Doi Numarası: 10.31801/cfsuasmas.877170
- Dergi Adı: COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.285-304
- Anahtar Kelimeler: Dual Lorentzian space, associated curves, dual general helix, dual slant helix, prin-cipal directed rectifying curve, SURFACES, HELICES
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Süleyman Demirel Üniversitesi Adresli: Evet
Özet
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).