Ruled Surfaces Constructed by the Involute-Evolute Curve with Sannia Frame

Süleyman Şenyurt; Hatice Yurttaş; Kemal Eren

doi:10.47000/tjmcs.1621463

Ruled Surfaces Constructed by the Involute-Evolute Curve with Sannia Frame

Abstract

In this study, ruled surfaces generated by the tangent, normal, and binormal vectors of the involute curve are investigated. Furthermore, the striction curve of each ruled surface is determined, and the Sannia frame defined along this curve is calculated. Subsequently, the normal vector fields of each surface, the first and second fundamental forms, and the Gaussian and mean curvatures are computed using the coefficients of these fundamental forms. At the end of the study, the developability and minimality of the surfaces are evaluated as results based on their Gaussian and mean curvatures. Additionally, examples of the surfaces are provided, and their graphs are plotted.

Keywords

References

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Kelleci, A., Eren, K., On the evolution of some associated type ruled surfaces, Mathematical Sciences and Applications E-Notes, 8(2020), 178–186.
Pressley, A., Elementary Differential Geometry. Second Edition, Springer London Ltd, London UK, 474s, 2010.
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Details

Primary Language

English

Subjects

Algebraic and Differential Geometry

Journal Section

Research Article

Authors

Süleyman Şenyurt
0000-0003-1097-5541
Türkiye

Hatice Yurttaş
0000-0002-0679-0977
Türkiye

Kemal Eren ^*
0000-0001-5273-7897
Türkiye

Publication Date

October 13, 2026

Submission Date

January 16, 2025

Acceptance Date

April 13, 2026

Published in Issue

Year 2026 Volume: 18 Number: 3

DOI

https://doi.org/10.47000/tjmcs.1621463

IZ

https://izlik.org/JA43BT43TR

Cite

RIS / Bibtex

APA

Şenyurt, S., Yurttaş, H., & Eren, K. (2026). Ruled Surfaces Constructed by the Involute-Evolute Curve with Sannia Frame. Turkish Journal of Mathematics and Computer Science, 18(3), 819-835. https://doi.org/10.47000/tjmcs.1621463

AMA

1.Şenyurt S, Yurttaş H, Eren K. Ruled Surfaces Constructed by the Involute-Evolute Curve with Sannia Frame. TJMCS. 2026;18(3):819-835. doi:10.47000/tjmcs.1621463

Chicago

Şenyurt, Süleyman, Hatice Yurttaş, and Kemal Eren. 2026. “Ruled Surfaces Constructed by the Involute-Evolute Curve With Sannia Frame”. Turkish Journal of Mathematics and Computer Science 18 (3): 819-35. https://doi.org/10.47000/tjmcs.1621463.

EndNote

Şenyurt S, Yurttaş H, Eren K (October 1, 2026) Ruled Surfaces Constructed by the Involute-Evolute Curve with Sannia Frame. Turkish Journal of Mathematics and Computer Science 18 3 819–835.

IEEE

[1]S. Şenyurt, H. Yurttaş, and K. Eren, “Ruled Surfaces Constructed by the Involute-Evolute Curve with Sannia Frame”, TJMCS, vol. 18, no. 3, pp. 819–835, Oct. 2026, doi: 10.47000/tjmcs.1621463.

ISNAD

Şenyurt, Süleyman - Yurttaş, Hatice - Eren, Kemal. “Ruled Surfaces Constructed by the Involute-Evolute Curve With Sannia Frame”. Turkish Journal of Mathematics and Computer Science 18/3 (October 1, 2026): 819-835. https://doi.org/10.47000/tjmcs.1621463.

JAMA

1.Şenyurt S, Yurttaş H, Eren K. Ruled Surfaces Constructed by the Involute-Evolute Curve with Sannia Frame. TJMCS. 2026;18:819–835.

MLA

Şenyurt, Süleyman, et al. “Ruled Surfaces Constructed by the Involute-Evolute Curve With Sannia Frame”. Turkish Journal of Mathematics and Computer Science, vol. 18, no. 3, Oct. 2026, pp. 819-35, doi:10.47000/tjmcs.1621463.

Vancouver

1.Süleyman Şenyurt, Hatice Yurttaş, Kemal Eren. Ruled Surfaces Constructed by the Involute-Evolute Curve with Sannia Frame. TJMCS. 2026 Oct. 1;18(3):819-35. doi:10.47000/tjmcs.1621463