Uzay-Benzeri Eğrilerin Serret-Frenet Çatısı Üzerine Analiz

Abstract

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.

Keywords

• Minkowski uzayı
• Serret Frenet
• uzay benzeri
• dönme açısı
• oskülatör düzlem

A Note on the Serret-Frenet Frame for Spacelike Curves

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.

Keywords

• Minkowski space
• Serret Frenet
• spacelike curves
• angle of rotation
• osculating plane

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