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Dergiler / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 71 Issue: 1

Associated curves of a Frenet curve in the dual Lorentzian space

Bahar Abalı(SÜLEYMAN DEMİREL ÜNİVERSİTESİ, FEN BİLİMLERİ ENSTİTÜSÜ)0000-0001-5900-6595
Ahmet Yücesan(Süleyman Demirel Üniversitesi)0000-0002-5419-925X
Sayfa
—
Yayın Tarihi
2022-03-30
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Finally, according to causal character of the principal donor curve of principal directed rectifying curve in $\mathbb{D}_{1}^{3}$, we show this curve to correspond to any timelike or spacelike ruled surface in Minkowski 3−space R 3 1 R13 .

📌 3 Maddede Bu Makale

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Amaç & Hipotez: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 3 1 D13 .
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Temel Bulgular & Veri:Then we show that the principal donor curve of a circle in $\mathbb{D}^{2}$ or a hyperbola in $\mathbb{D}_{1}^{2}$ and the principal directed curve of a slant helix in $\mathbb{D}_{1}^{3}$ are a helix and general helix, respectively.
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Sonuç & Katkı:Finally, according to causal character of the principal donor curve of principal directed rectifying curve in $\mathbb{D}_{1}^{3}$, we show this curve to correspond to any timelike or spacelike ruled surface in Minkowski 3−space R 3 1 R13 .
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Dual Lorentzian space · associated curves · dual general helix

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 3 1 D13 . 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 $\mathbb{D}^{2}$ or a hyperbola in $\mathbb{D}_{1}^{2}$ and the principal directed curve of a slant helix in $\mathbb{D}_{1}^{3}$ 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 $\mathbb{D}_{1}^{3}$, we show this curve to correspond to any timelike or spacelike ruled surface in Minkowski 3−space R 3 1 R13 .

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Bu Makaleye Atıf Yap

Abalı, B., Yücesan, A. (2022). Associated curves of a Frenet curve in the dual Lorentzian space. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 71 Issue: 1. https://doi.org/10.31801/cfsuasmas.877170

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Kaynakça (21)

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