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Journals / Muş Alparslan Üniversitesi Fen Bilimleri Dergisi / 2026 / Cilt: 14 Sayı: 1

A Note on the Serret-Frenet Frame for Spacelike Curves

Uzay-Benzeri Eğrilerin Serret-Frenet Çatısı Üzerine Analiz

Selcan Kocabas(Kırklareli University, Institute of Science)0000-0003-3416-9608
Pages
183–190
Publication Date
2026-06-27
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, illustrative examples are presented together with their graphical representations.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, a system of equations is introduced to characterize spacelike curves with timelike principal normal vector field in three‑dimensional Minkowski space.
📊
Key Findings & Data:The formulation expresses the Serret-Frenet equations with respect to the curvature κ and a rotation angle θ around the osculating plane, providing a structured representation of the Serret-Frenet system through these quantities.
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Conclusion & Impact:Finally, illustrative examples are presented together with their graphical representations.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Minkowski uzayı · Serret Frenet · uzay benzeri

Abstract

In this study, a system of equations is introduced to characterize spacelike curves with timelike principal normal vector field in three‑dimensional Minkowski space. The formulation expresses the Serret-Frenet equations with respect to the curvature κ and a rotation angle θ around the osculating plane, providing a structured representation of the Serret-Frenet system through these quantities. Moreover, the cases in which κ or θ are constant are analyzed explicitly, and the expressions for the tangent vector field and torsion are obtained. Finally, illustrative examples are presented together with their graphical representations.

Özet

Bu çalışmada, üç boyutlu Minkowski uzayında zaman‑benzeri asal normal vektör alanına sahip uzay‑benzeri eğrileri karakterize eden bir denklem sistemi ortaya konulmuştur. Geliştirilen formülasyon, Serret–Frenet elemanlarının 𝜅 eğrilik fonksiyonu ve 𝜃 dönme açısı cinsinden sistematik bir gösterimini sağlamaktadır. Ayrıca, 𝜅 veya 𝜃 değerlerinin sabit olduğu durumlar açık bir biçimde incelenmiş; teğet vektör alanı ile burulma fonksiyonuna ilişkin ifadeler elde edilmiştir. Son olarak, elde edilen sonuçlar grafik gösterimleriyle birlikte örneklendirilmiştir.

🔖

Cite This Article

Kocabas, S. (2026). A Note on the Serret-Frenet Frame for Spacelike Curves. Muş Alparslan Üniversitesi Fen Bilimleri Dergisi, Cilt: 14 Sayı: 1, 183–190. https://doi.org/10.18586/msufbd.1920077

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