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Journals / International Electronic Journal of Geometry / 2025 / Volume: 18 Issue: 2

Quaternionic Framed Bertrand Curves

Ayşe Zeynep Azak(SAKARYA ÜNİVERSİTESİ)0000-0002-2686-6043
Arzu Sürekçi(SAKARYA UYGULAMALI BİLİMLER ÜNİVERSİTESİ)0000-0003-2003-3507
Mehmet Ali Güngör(SAKARYA ÜNİVERSİTESİ)0000-0003-1863-3183
Pages
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Publication Date
2025-10-19
DOI
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AI Summary & Key Takeaways

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

Finally, an example has been given that supports the proven theorem in our study.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:There is no pair of Bertrand quaternionic curves in the classical sense in quaternionic space.
📊
Key Findings & Data:Then, we demonstrate that Bertrand’s partner of any framed quaternionic curve is a framed quaternionic curve.
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Conclusion & Impact:Finally, an example has been given that supports the proven theorem in our study.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Singular curve · Bertrand curves · quaternionic curve

Abstract

There is no pair of Bertrand quaternionic curves in the classical sense in quaternionic space. Therefore, realizing that investigating singular points and analyzing their properties and behavior is a rising topic in differential geometry, framed Bertrand mates, which are singular have been defined in the quaternionic space. The characteristic properties of these curves have been given. Thus, we have proven that the distance between these pairs of curves remains constant. The conditions for framed quaternionic curves to be Bertrand mates have been shown. Then, we demonstrate that Bertrand’s partner of any framed quaternionic curve is a framed quaternionic curve. Furthermore, the relationship between the curvatures of quaternionic framed Bertrand curves has been given. Finally, an example has been given that supports the proven theorem in our study.

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Cite This Article

Azak, A. Z., Sürekçi, A., Güngör, M. A. (2025). Quaternionic Framed Bertrand Curves. International Electronic Journal of Geometry, Volume: 18 Issue: 2. https://ajindex.com/articles/1410911

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