Serret-Frenet Formula of Quaternionic Framed Curves

Zülal Derin Yaqub; Mehmet Ali Güngör

doi:10.36753/mathenot.1658156

EN

Serret-Frenet Formula of Quaternionic Framed Curves

Abstract

In this study, we present an approach by introducing the quaternionic structure of framed curves. Furthermore, we derive Serret-Frenet formulas and give specific results for quaternionic framed curves. Initially, we focus on the moving frame and its curvatures corresponding to the frame $ T,N,B $ along the quaternionic framed base curve in three-dimensional Euclidean space ${\mathbb{R}^3}$. Then, we establish the Serret-Frenet type formulas of quaternionic framed curves. We then generalize these formulas and the definition of quaternionic framed curves to four-dimensional Euclidean space, highlighting the relationship between the curvatures in both 3-dimensional and four-dimensional Euclidean spaces. In addition, the theorems are supported by examples, demonstrating the applicability of the proposed results.

Keywords

Framed curves, Serret-Frenet formulas, Singular point, Quaternion

Thanks

The authors would like to express their sincere thanks to the editor and the anonymous reviewers for their helpful comments and suggestions.

References

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Details

Primary Language

English

Subjects

Applied Mathematics (Other)

Journal Section

Research Article

Authors

Zülal Derin Yaqub ^*
0000-0001-9712-0428
Türkiye

Mehmet Ali Güngör
0000-0003-1863-3183
Türkiye

Early Pub Date

June 20, 2025

Publication Date

June 26, 2025

Submission Date

March 14, 2025

Acceptance Date

June 14, 2025

Published in Issue

Year 2025 Volume: 13 Number: 2

DOI

https://doi.org/10.36753/mathenot.1658156

IZ

https://izlik.org/JA75EP22KS

APA

Derin Yaqub, Z., & Güngör, M. A. (2025). Serret-Frenet Formula of Quaternionic Framed Curves. Mathematical Sciences and Applications E-Notes, 13(2), 92-105. https://doi.org/10.36753/mathenot.1658156

AMA

1.Derin Yaqub Z, Güngör MA. Serret-Frenet Formula of Quaternionic Framed Curves. Math. Sci. Appl. E-Notes. 2025;13(2):92-105. doi:10.36753/mathenot.1658156

Chicago

Derin Yaqub, Zülal, and Mehmet Ali Güngör. 2025. “Serret-Frenet Formula of Quaternionic Framed Curves”. Mathematical Sciences and Applications E-Notes 13 (2): 92-105. https://doi.org/10.36753/mathenot.1658156.

EndNote

Derin Yaqub Z, Güngör MA (June 1, 2025) Serret-Frenet Formula of Quaternionic Framed Curves. Mathematical Sciences and Applications E-Notes 13 2 92–105.

IEEE

[1]Z. Derin Yaqub and M. A. Güngör, “Serret-Frenet Formula of Quaternionic Framed Curves”, Math. Sci. Appl. E-Notes, vol. 13, no. 2, pp. 92–105, June 2025, doi: 10.36753/mathenot.1658156.

ISNAD

Derin Yaqub, Zülal - Güngör, Mehmet Ali. “Serret-Frenet Formula of Quaternionic Framed Curves”. Mathematical Sciences and Applications E-Notes 13/2 (June 1, 2025): 92-105. https://doi.org/10.36753/mathenot.1658156.

JAMA

1.Derin Yaqub Z, Güngör MA. Serret-Frenet Formula of Quaternionic Framed Curves. Math. Sci. Appl. E-Notes. 2025;13:92–105.

MLA

Derin Yaqub, Zülal, and Mehmet Ali Güngör. “Serret-Frenet Formula of Quaternionic Framed Curves”. Mathematical Sciences and Applications E-Notes, vol. 13, no. 2, June 2025, pp. 92-105, doi:10.36753/mathenot.1658156.

Vancouver

1.Zülal Derin Yaqub, Mehmet Ali Güngör. Serret-Frenet Formula of Quaternionic Framed Curves. Math. Sci. Appl. E-Notes. 2025 Jun. 1;13(2):92-105. doi:10.36753/mathenot.1658156