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

Ferdağ Kahraman Aksoyak

doi:10.31801/cfsuasmas.1650280

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

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.

Keywords

References

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Details

Primary Language

English

Subjects

Algebraic and Differential Geometry

Journal Section

Research Article

Authors

Ferdağ Kahraman Aksoyak ^*
0000-0003-4633-034X
Türkiye

Publication Date

September 23, 2025

Submission Date

March 3, 2025

Acceptance Date

May 15, 2025

Published in Issue

Year 2025 Volume: 74 Number: 3

DOI

https://doi.org/10.31801/cfsuasmas.1650280

IZ

https://izlik.org/JA69BF32FC

Cite

RIS / Bibtex

APA

Kahraman Aksoyak, F. (2025). Quaternionic Sabban frame in $\mathbb{R}^{3}$ and $\mathbb{R}^{4}$. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 74(3), 513-522. https://doi.org/10.31801/cfsuasmas.1650280

AMA

1.Kahraman Aksoyak F. Quaternionic Sabban frame in $\mathbb{R}^{3}$ and $\mathbb{R}^{4}$. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2025;74(3):513-522. doi:10.31801/cfsuasmas.1650280

Chicago

Kahraman Aksoyak, Ferdağ. 2025. “Quaternionic Sabban Frame in $\mathbb{R}^{3}$ and $\mathbb{R}^{4}$”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 74 (3): 513-22. https://doi.org/10.31801/cfsuasmas.1650280.

EndNote

Kahraman Aksoyak F (September 1, 2025) Quaternionic Sabban frame in $\mathbb{R}^{3}$ and $\mathbb{R}^{4}$. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 74 3 513–522.

IEEE

[1]F. Kahraman Aksoyak, “Quaternionic Sabban frame in $\mathbb{R}^{3}$ and $\mathbb{R}^{4}$”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 74, no. 3, pp. 513–522, Sept. 2025, doi: 10.31801/cfsuasmas.1650280.

ISNAD

Kahraman Aksoyak, Ferdağ. “Quaternionic Sabban Frame in $\mathbb{R}^{3}$ and $\mathbb{R}^{4}$”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 74/3 (September 1, 2025): 513-522. https://doi.org/10.31801/cfsuasmas.1650280.

JAMA

1.Kahraman Aksoyak F. Quaternionic Sabban frame in $\mathbb{R}^{3}$ and $\mathbb{R}^{4}$. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2025;74:513–522.

MLA

Kahraman Aksoyak, Ferdağ. “Quaternionic Sabban Frame in $\mathbb{R}^{3}$ and $\mathbb{R}^{4}$”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 74, no. 3, Sept. 2025, pp. 513-22, doi:10.31801/cfsuasmas.1650280.

Vancouver

1.Ferdağ Kahraman Aksoyak. Quaternionic Sabban frame in $\mathbb{R}^{3}$ and $\mathbb{R}^{4}$. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2025 Sep. 1;74(3):513-22. doi:10.31801/cfsuasmas.1650280