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Journals / International Electronic Journal of Geometry / 2026 / Volume: 19 Issue: 2

Generalized Tzitzeica Curves with Myller Configuration

Zehra İşbilir(DUZCE UNIVERSITY, FACULTY OF ARTS AND SCIENCES)0000-0001-5414-5887
Bahar Doğan Yazıcı(BILECIK SEYH EDEBALI UNIVERSITY)0000-0001-5690-4840
Murat Tosun(SAKARYA UNIVERSITY)0000-0002-4888-1412
Pages
—
Publication Date
2026-10-25
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Then, we give some properties related to the Salkowski-type, anti-Salkowski-type, and $\overline{\xi}_2$-constant Tzitzeica curves.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, our aim is to investigate the Tzitzeica curves with Frenet-type frame for Myller configuration in 3D Euclidean space $\mathbb{E}_3$.
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Key Findings & Data:Frenet-type frame with Myller configuration in $\mathbb{E}_3$ is a natural generalization for classical Frenet frame in $\mathbb{E}_3$ due to the natural and unique construction of Myller configuration in $\mathbb{E}_3$.
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Conclusion & Impact:Then, we give some properties related to the Salkowski-type, anti-Salkowski-type, and $\overline{\xi}_2$-constant Tzitzeica curves.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Frenet-type frame · Myller configuration · Tzitzeica curves

Abstract

In this study, our aim is to investigate the Tzitzeica curves with Frenet-type frame for Myller configuration in 3D Euclidean space $\mathbb{E}_3$. Frenet-type frame with Myller configuration in $\mathbb{E}_3$ is a natural generalization for classical Frenet frame in $\mathbb{E}_3$ due to the natural and unique construction of Myller configuration in $\mathbb{E}_3$. According to this relation, we derive a general Tzitzeica curves with Frenet-type frame for Myller configuration, which includes not only the Frenet frame in $\mathbb{E}_3$ as a special case in the existing literature and several special cases, as well. Additionally, we characterize them based on the curvatures. Then, we give some properties related to the Salkowski-type, anti-Salkowski-type, and $\overline{\xi}_2$-constant Tzitzeica curves.

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Cite This Article

İşbilir, Z., Yazıcı, B. D., Tosun, M. (2026). Generalized Tzitzeica Curves with Myller Configuration. International Electronic Journal of Geometry, Volume: 19 Issue: 2. https://doi.org/10.36890/iejg.1922581

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