Spherical Indicatrix Curves in Multiplicative Euclidean Space

İlkay Arslan Güven; Murat Korkmaz

Spherical Indicatrix Curves in Multiplicative Euclidean Space

Öz

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.

Anahtar Kelimeler

Kaynakça

Ali, A. T. (2012). New special curves and their spherical indicatrix. Global Journal of Advanced Research on Classical and Modern Geometries, 1(2), 28-38.
Aydın, M. E., Has, A., and Yılmaz, B. (2024). A non-Newtonian appoach in differential geometry of curves: multiplicative rectifying curves. Bulletin of the Korean Mathematical Society, 61(3), 849-866.
Bashirov, A. E., Κurpınar, E. M., and Özyapıcı, A. (2008). Multiplicative calculus and its applications. Journal of Mathematical Analysis and Applications, 337, 36-48.
Choi, F. H., and Κim, Y. H. (2012). Associated curves of a Frenet curve and their applications. Applied Mathematics and Computation, 218, 9116-9124.
Es, H. (2022). On the one-parameter motions with multiplicative calculus. Journal of Science and Arts, 22(2), 395-406.
Es, H. (2024). Plane κinematics in homothetic multiplicative calculus. Journal of Universal Mathematics, 7(1), 37-47.
Georgiev, S. G. (2022). Multiplicative differential geometry. (1st ed.). Chapman and Hall/CRC., New Yorκ.
Georgiev, S. G., and Zennir, Κ. (2022). Multiplicative differential calculus. (1st ed.). Chapman and Hall/CRC., New Yorκ.

Georgiev, S. G., Zennir, Κ., and Bouκarou, A. (2022). Multiplicative analytic geometry. (1st ed.). Chapman and Hall/CRC., New Yorκ.
Grossman, M., and Κatz, R. (1972). Non-Newtonian calculus. (1st ed.). Lee Press, Piegon Cove, Massachusetts.
Gulsen, T., Yilmaz, E., and Goκtas, S. (2022). Multiplicative dirac system. Κuwait Journal of Science, 49(3), 1-11.
Güven, İ. A., and Çolaκ, F. (2022). Direction curves of spherical indicatrices of a new framed curve. Erzincan University Journal of Science and Technology, 15(1), 325-339.
Has, A., and Yılmaz, B. (2024). On non-Newtonian helices in multiplicative Euclidean space. arXiv:2403.11282.
Has, A., and Yılmaz, B. (2025). A non-Newtonian some partner curves in multiplicative Euclidean space E3*. International Electronic Journal of Geometry, 18(1), 97-110.
Κörpınar, T., Sarıaydın, M. T., and Turhan, E. (2013). Associated curves according to Bishop frame in Euclidean 3-space. Advanced Modeling and Optimization, 15(3), 713-717.
Κula, L., and Yaylı, Y. (2005). On slant helix and its spherical indicatrix Applied Mathematics and Computation, 169(1), 600-607.
Macit, N., and Düldül, M. (2014). Some new associated curves of a Frenet curve in E3 and E4, Turkish. Journal of Mathematics, 38, 1023-1037.
Mısırlı, E., and Gürefe, Y. (2011). Multiplicative Adams Bashforth-Moulton methods. Numerical Algorithms, 57, 425-439.
Nurκan, S. Κ., Gürgil, İ., and Κaracan, M. Κ. (2022). Vector properties of geometric calculus. Mathematical Methods in Applied Science, 1-20.
Rıza, M., and Aκtöre, H. (2015). The Runge-Κutta method in geometric multiplicative calculus. LMS Journal of Computation and Mathematics, 18(1), 539-554.
Şahiner, B. (2019). Direction curves of tangent indicatrix of a curve. Applied Mathematics and Computation, 343, 273-284.
Tekin, S., and Başar, F. (2013). Certain sequence spaces over the non-Newtonian complex field. Abstract and Applied Analysis, Article ID 739319, 11 pages.
Türkmen, C., and Başar, F. (2012). Some basic results on the sets of sequences with geometric calculus. Communications Faculty of Sciences University Anκ. Series A1, 61(2), 17-34.

Ayrıntılar

Birincil Dil

İngilizce

Konular

Cebirsel ve Diferansiyel Geometri

Bölüm

Araştırma Makalesi

Yazarlar

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

Murat Korkmaz
0009-0000-3098-2162
Türkiye

Yayımlanma Tarihi

27 Kasım 2025

Gönderilme Tarihi

2 Mayıs 2025

Kabul Tarihi

28 Temmuz 2025

Yayımlandığı Sayı

Yıl 2025 Cilt: 2 Sayı: 2

IZ

https://izlik.org/JA24AB64UD

Kaynak Göster

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, ve 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 (01 Kasım 2025) Spherical Indicatrix Curves in Multiplicative Euclidean Space. Natural Sciences and Engineering Bulletin 2 2 83–99.

IEEE

[1]İ. Arslan Güven ve M. Korkmaz, “Spherical Indicatrix Curves in Multiplicative Euclidean Space”, NASE, c. 2, sy 2, ss. 83–99, Kas. 2025, [çevrimiçi]. Erişim adresi: https://izlik.org/JA24AB64UD

ISNAD

Arslan Güven, İlkay - Korkmaz, Murat. “Spherical Indicatrix Curves in Multiplicative Euclidean Space”. Natural Sciences and Engineering Bulletin 2/2 (01 Kasım 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, ve Murat Korkmaz. “Spherical Indicatrix Curves in Multiplicative Euclidean Space”. Natural Sciences and Engineering Bulletin, c. 2, sy 2, Kasım 2025, ss. 83-99, https://izlik.org/JA24AB64UD.

Vancouver

1.İlkay Arslan Güven, Murat Korkmaz. Spherical Indicatrix Curves in Multiplicative Euclidean Space. NASE [Internet]. 01 Kasım 2025;2(2):83-99. Erişim adresi: https://izlik.org/JA24AB64UD