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Journals / Konuralp Journal of Mathematics / 2026 / Volume: 14 Issue: 1

On Characterizations of Osculating Curves using Darboux Frame in Minkowski 3-Space

Kemal Eren(Sakarya Üniversitesi Matematik Bölümü, Sakarya.Türkiye)0000-0001-5273-7897
Mahmutcan Carlı(ORDU UNIVERSITY)
Soley Ersoy(SAKARYA UNIVERSITY)0000-0002-7183-7081
Pages
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Publication Date
2026-04-30
DOI
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AI Summary & Key Takeaways

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

Finally, illustrative examples supporting the theoretical results are presented, and graphical visualizations of the obtained curves are provided to demonstrate their geometric behavior.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we investigate osculating curves in Minkowski 3-space by means of the Darboux frame associated with a non-null curve lying on a surface.
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Key Findings & Data:Moreover, we introduce and construct two distinct classes of osculating curves, namely type-1 and type-2 osculating curves.
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Conclusion & Impact:Finally, illustrative examples supporting the theoretical results are presented, and graphical visualizations of the obtained curves are provided to demonstrate their geometric behavior.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Darboux frame · osculating curve · geodesic torsion

Abstract

In this paper, we investigate osculating curves in Minkowski 3-space by means of the Darboux frame associated with a non-null curve lying on a surface. Moreover, we introduce and construct two distinct classes of osculating curves, namely type-1 and type-2 osculating curves. Using the Darboux frame, we derive necessary and sufficient conditions under which a non-null curve lying on a surface becomes an osculating curve, expressed in terms of the geodesic curvature ${k_g}$, normal curvature ${k_n}$, and geodesic torsion ${\tau _g}$. As a consequence of these conditions, several corollaries and theorems concerning type-1 and type-2 osculating curves are established. Finally, illustrative examples supporting the theoretical results are presented, and graphical visualizations of the obtained curves are provided to demonstrate their geometric behavior.

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Cite This Article

Eren, K., Carlı, M., Ersoy, S. (2026). On Characterizations of Osculating Curves using Darboux Frame in Minkowski 3-Space. Konuralp Journal of Mathematics, Volume: 14 Issue: 1. https://ajindex.com/articles/1521447

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