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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 72 Issue: 3

On special singular curve couples of framed curves in 3D Lie groups

Bahar Doğan Yazıcı(BİLECİK ŞEYH EDEBALİ ÜNİVERSİTESİ)0000-0001-5690-4840
Osman Zeki Okuyucu(BİLECİK ŞEYH EDEBALİ ÜNİVERSİTESİ)0000-0003-4379-0252
Murat Tosun(SAKARYA ÜNİVERSİTESİ)0000-0002-4888-1412
Pages
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Publication Date
2023-09-30
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AI Summary & Key Takeaways

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

In addition, we obtain the characterization of Bertrand and Mannheim curves according to the various frames of framed curves in 3D Lie groups.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we introduce Bertrand and Mannheim curves of framed curves, which are a special singular curve in 3D Lie groups.
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Key Findings & Data:We explain the conditions for framed curves to be Bertrand curves and Mannheim curves in 3D Lie groups.
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Conclusion & Impact:In addition, we obtain the characterization of Bertrand and Mannheim curves according to the various frames of framed curves in 3D Lie groups.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Bertrand curves · Mannheim curves · framed curves

Abstract

In this paper, we introduce Bertrand and Mannheim curves of framed curves, which are a special singular curve in 3D Lie groups. We explain the conditions for framed curves to be Bertrand curves and Mannheim curves in 3D Lie groups. We give relationships between framed curvatures and Lie curvatures of Bertrand and Mannheim curves of framed curves. In addition, we obtain the characterization of Bertrand and Mannheim curves according to the various frames of framed curves in 3D Lie groups.

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Cite This Article

Yazıcı, B. D., Okuyucu, O. Z., Tosun, M. (2023). On special singular curve couples of framed curves in 3D Lie groups. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 72 Issue: 3. https://doi.org/10.31801/cfsuasmas.1197154

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