DOI: 10.36890/iejg.1922581 ISSN: 1307-5624

Generalized Tzitzeica Curves with Myller Configuration

Zehra İşbilir, Bahar Doğan Yazıcı, Murat Tosun
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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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