Tzitzeica Curves According to Modified Orthogonal Frames

Esra Damar

doi:10.17776/csj.1751734

Tzitzeica Curves According to Modified Orthogonal Frames

Abstract

This paper explores Tzitzeica curves in three-dimensional Euclidean space through the use of modified orthogonal frames constructed via curvature and torsion functions. First, the fundamental differences between the classical Frenet frame and the modified orthogonal frame are clarified. Following this, the necessary and sufficient conditions under which a curve can be classified as a Tzitzeica curve relative to the modified frame are established. The study also presents characterization theorems for spherical Tzitzeica curves and Tz-general helices, supported by differential geometric expressions involving curvature and torsion functions. Furthermore, special cases such as anti-Salkowski curves and rectifying curves are examined.

Keywords

Modified orthogonal frame, Spherical curves, Tzitzeica curves

References

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Details

Primary Language

English

Subjects

Algebraic and Differential Geometry

Journal Section

Research Article

Authors

Esra Damar ^*
0000-0002-0743-8545
Türkiye

Publication Date

September 30, 2025

Submission Date

July 26, 2025

Acceptance Date

September 22, 2025

Published in Issue

Year 2025 Volume: 46 Number: 3

DOI

https://doi.org/10.17776/csj.1751734

IZ

https://izlik.org/JA35BM67BU

APA

Damar, E. (2025). Tzitzeica Curves According to Modified Orthogonal Frames. Cumhuriyet Science Journal, 46(3), 595-600. https://doi.org/10.17776/csj.1751734

AMA

1.Damar E. Tzitzeica Curves According to Modified Orthogonal Frames. CSJ. 2025;46(3):595-600. doi:10.17776/csj.1751734

Chicago

Damar, Esra. 2025. “Tzitzeica Curves According to Modified Orthogonal Frames”. Cumhuriyet Science Journal 46 (3): 595-600. https://doi.org/10.17776/csj.1751734.

EndNote

Damar E (September 1, 2025) Tzitzeica Curves According to Modified Orthogonal Frames. Cumhuriyet Science Journal 46 3 595–600.

IEEE

[1]E. Damar, “Tzitzeica Curves According to Modified Orthogonal Frames”, CSJ, vol. 46, no. 3, pp. 595–600, Sept. 2025, doi: 10.17776/csj.1751734.

ISNAD

Damar, Esra. “Tzitzeica Curves According to Modified Orthogonal Frames”. Cumhuriyet Science Journal 46/3 (September 1, 2025): 595-600. https://doi.org/10.17776/csj.1751734.

JAMA

1.Damar E. Tzitzeica Curves According to Modified Orthogonal Frames. CSJ. 2025;46:595–600.

MLA

Damar, Esra. “Tzitzeica Curves According to Modified Orthogonal Frames”. Cumhuriyet Science Journal, vol. 46, no. 3, Sept. 2025, pp. 595-00, doi:10.17776/csj.1751734.

Vancouver

1.Esra Damar. Tzitzeica Curves According to Modified Orthogonal Frames. CSJ. 2025 Sep. 1;46(3):595-600. doi:10.17776/csj.1751734

Cited By

Characterization of Tzitzeica Curves by Using q-frame in Euclidean 3-space

Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi

https://doi.org/10.19113/sdufenbed.1805264

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