Ruled Invariants and Ruled Surfaces Created with Spherical Curves in Galilean Space

Keziban Orbay; Duygu Aydoğan; Tevfik Şahin

doi:10.17798/bitlisfen.1824791

Ruled Invariants and Ruled Surfaces Created with Spherical Curves in Galilean Space

Abstract

This study aims to examine the ruled invariants of ruled surfaces in three-dimensional Galilean space G_3, where the direction vector is determined by a curve lying on the Galilean central unit sphere. The main goal is to derive ruled invariants of such surfaces by employing a geometric approach rooted in the properties of spherical curves. To achieve this, we first compute the orthonormal frame and corresponding derivative equations of a curve lying on the surface of the Galilean central unit sphere. Then, structure functions and ruled invariants are defined and obtained in Galilean geometry sense. The study covers all three types of ruled surfaces in Galilean space. Additionally, the relationships between the Frenet frames of the curves and those of the ruled surfaces are examined in a systematic manner. The findings provide insight into the intrinsic properties of ruled surfaces and contribute to the broader understanding of geometry in non-Euclidean settings.

Keywords

Supporting Institution

No supporting institution

Ethical Statement

The study is complied with research and publication ethics.

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Details

Primary Language

English

Subjects

Algebraic and Differential Geometry

Journal Section

Research Article

Authors

Keziban Orbay ^*
0000-0002-7642-4139
Türkiye

Duygu Aydoğan
0009-0009-2906-4669
Türkiye

Tevfik Şahin
0000-0001-7598-5842
Türkiye

Publication Date

March 24, 2026

Submission Date

November 16, 2025

Acceptance Date

February 8, 2026

Published in Issue

Year 2026 Volume: 15 Number: 1

DOI

https://doi.org/10.17798/bitlisfen.1824791

IZ

https://izlik.org/JA82UR37GX

Cite

RIS / Bibtex

APA

Orbay, K., Aydoğan, D., & Şahin, T. (2026). Ruled Invariants and Ruled Surfaces Created with Spherical Curves in Galilean Space. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, 15(1), 394-407. https://doi.org/10.17798/bitlisfen.1824791

AMA

1.Orbay K, Aydoğan D, Şahin T. Ruled Invariants and Ruled Surfaces Created with Spherical Curves in Galilean Space. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi. 2026;15(1):394-407. doi:10.17798/bitlisfen.1824791

Chicago

Orbay, Keziban, Duygu Aydoğan, and Tevfik Şahin. 2026. “Ruled Invariants and Ruled Surfaces Created With Spherical Curves in Galilean Space”. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi 15 (1): 394-407. https://doi.org/10.17798/bitlisfen.1824791.

EndNote

Orbay K, Aydoğan D, Şahin T (March 1, 2026) Ruled Invariants and Ruled Surfaces Created with Spherical Curves in Galilean Space. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi 15 1 394–407.

IEEE

[1]K. Orbay, D. Aydoğan, and T. Şahin, “Ruled Invariants and Ruled Surfaces Created with Spherical Curves in Galilean Space”, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, vol. 15, no. 1, pp. 394–407, Mar. 2026, doi: 10.17798/bitlisfen.1824791.

ISNAD

Orbay, Keziban - Aydoğan, Duygu - Şahin, Tevfik. “Ruled Invariants and Ruled Surfaces Created With Spherical Curves in Galilean Space”. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi 15/1 (March 1, 2026): 394-407. https://doi.org/10.17798/bitlisfen.1824791.

JAMA

1.Orbay K, Aydoğan D, Şahin T. Ruled Invariants and Ruled Surfaces Created with Spherical Curves in Galilean Space. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi. 2026;15:394–407.

MLA

Orbay, Keziban, et al. “Ruled Invariants and Ruled Surfaces Created With Spherical Curves in Galilean Space”. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, vol. 15, no. 1, Mar. 2026, pp. 394-07, doi:10.17798/bitlisfen.1824791.

Vancouver

1.Keziban Orbay, Duygu Aydoğan, Tevfik Şahin. Ruled Invariants and Ruled Surfaces Created with Spherical Curves in Galilean Space. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi. 2026 Mar. 1;15(1):394-407. doi:10.17798/bitlisfen.1824791

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Journal of New Results in Science

https://doi.org/10.54187/jnrs.1797734