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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 74 Issue: 3

Quaternionic Sabban frame in $\mathbb{R}^{3}$ and $\mathbb{R}^{4}$

Ferdağ Kahraman Aksoyak(KIRŞEHİR AHİ EVRAN ÜNİVERSİTESİ)0000-0003-4633-034X
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Publication Date
2025-09-23
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AI Summary & Key Takeaways

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

Also, we support the theory in the paper with some examples.

📌 3 Key Takeaways

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Objective & Hypothesis:In this paper, we first reconsider Sabban frame of curves on $2-$sphere $S^{2}$ in $\mathbb{R}^{3}$ with the help of the properties of quaternion algebra and then, we define two different types of quaternionic Sabban frame of the curves on $3$-sphere $S^{3}$ in $\mathbb{R}^{4}$.
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Key Findings & Data:In this paper, we first reconsider Sabban frame of curves on $2-$sphere $S^{2}$ in $\mathbb{R}^{3}$ with the help of the properties of quaternion algebra and then, we define two different types of quaternionic Sabban frame of the curves on $3$-sphere $S^{3}$ in $\mathbb{R}^{4}$.
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Conclusion & Impact:Also, we support the theory in the paper with some examples.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Quaternions · quaternionic frame · Sabban frame

Abstract

In this paper, we first reconsider Sabban frame of curves on $2-$sphere $S^{2}$ in $\mathbb{R}^{3}$ with the help of the properties of quaternion algebra and then, we define two different types of quaternionic Sabban frame of the curves on $3$-sphere $S^{3}$ in $\mathbb{R}^{4}$. Also, we support the theory in the paper with some examples.

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Cite This Article

Aksoyak, F. K. (2025). Quaternionic Sabban frame in $\mathbb{R}^{3}$ and $\mathbb{R}^{4}$. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 74 Issue: 3. https://doi.org/10.31801/cfsuasmas.1650280

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