Spherical Indicatrix Curves in Multiplicative Euclidean Space

İlkay Arslan Güven; Murat Korkmaz

Spherical Indicatrix Curves in Multiplicative Euclidean Space

Abstract

The goal of this study is to investigate spherical indicatrix curves in multiplicative space R_*. Spherical indicatrix curves that develop on the surface of sphere, are one of the type of associated curves. By considering the multiplicative Frenet frame of a multiplicative curve in three dimensional multiplicative Euclidean space, there are three multiplicative indicatrix curves: tangent indicatrix, principal normal indicatrix and binormal indicatrix curves. We obtain the Frenet apparatus of these curves in terms of multiplicative derivative and calculations and give some characterizations about being multiplicative Bertrand and involute-evolute curve pairs between the indicatrix curves. We also demonstrate relations between the main multiplicative curve and indicatrix curves. Lastly, we exemplify with the figures which supports the theory in this study.

Keywords

References

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Details

Primary Language

English

Subjects

Algebraic and Differential Geometry

Journal Section

Research Article

Authors

İlkay Arslan Güven ^*
0000-0002-5302-6074
Türkiye

Murat Korkmaz
0009-0000-3098-2162
Türkiye

Publication Date

November 27, 2025

Submission Date

May 2, 2025

Acceptance Date

July 28, 2025

Published in Issue

Year 2025 Volume: 2 Number: 2

IZ

https://izlik.org/JA24AB64UD

Cite

RIS / Bibtex

APA

Arslan Güven, İ., & Korkmaz, M. (2025). Spherical Indicatrix Curves in Multiplicative Euclidean Space. Natural Sciences and Engineering Bulletin, 2(2), 83-99. https://izlik.org/JA24AB64UD

AMA

1.Arslan Güven İ, Korkmaz M. Spherical Indicatrix Curves in Multiplicative Euclidean Space. NASE. 2025;2(2):83-99. https://izlik.org/JA24AB64UD

Chicago

Arslan Güven, İlkay, and Murat Korkmaz. 2025. “Spherical Indicatrix Curves in Multiplicative Euclidean Space”. Natural Sciences and Engineering Bulletin 2 (2): 83-99. https://izlik.org/JA24AB64UD.

EndNote

Arslan Güven İ, Korkmaz M (November 1, 2025) Spherical Indicatrix Curves in Multiplicative Euclidean Space. Natural Sciences and Engineering Bulletin 2 2 83–99.

IEEE

[1]İ. Arslan Güven and M. Korkmaz, “Spherical Indicatrix Curves in Multiplicative Euclidean Space”, NASE, vol. 2, no. 2, pp. 83–99, Nov. 2025, [Online]. Available: https://izlik.org/JA24AB64UD

ISNAD

Arslan Güven, İlkay - Korkmaz, Murat. “Spherical Indicatrix Curves in Multiplicative Euclidean Space”. Natural Sciences and Engineering Bulletin 2/2 (November 1, 2025): 83-99. https://izlik.org/JA24AB64UD.

JAMA

1.Arslan Güven İ, Korkmaz M. Spherical Indicatrix Curves in Multiplicative Euclidean Space. NASE. 2025;2:83–99.

MLA

Arslan Güven, İlkay, and Murat Korkmaz. “Spherical Indicatrix Curves in Multiplicative Euclidean Space”. Natural Sciences and Engineering Bulletin, vol. 2, no. 2, Nov. 2025, pp. 83-99, https://izlik.org/JA24AB64UD.

Vancouver

1.İlkay Arslan Güven, Murat Korkmaz. Spherical Indicatrix Curves in Multiplicative Euclidean Space. NASE [Internet]. 2025 Nov. 1;2(2):83-99. Available from: https://izlik.org/JA24AB64UD