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Journals / Hagia Sophia Journal of Geometry / 2022 / Cilt: 4 Sayı: 2

The Frenet Vectors and the Curvatures of Curves $\mathit{{\mathbf{N-T^{\ast }B^{\ast }}}}$ in $\mathbf{E}^{3}$

Şeyda Kılıçoglu(BASKENT UNIVERSITY)0000-0003-0252-1574
Süleyman Şenyurt(ORDU UNIVERSITY)0000-0003-1097-5541
Sümeyye Gür Mazlum(Gümüşhane Üniversitesi)0000-0003-2471-1627
Pages
11–18
Publication Date
2022-12-30
DOI
—
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AI Summary & Key Takeaways

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

And we express the Frenet vectors and the curvatures of the curve $\beta^*$ in terms of the Frenet vectors and the curvatures of the curve $\beta$.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we describe a new pair of curves where the principal normal vector of a curve $\beta$ and an vector $R^*$ lying in the rectifian plane of a curve $\beta^*$ are linearly dependent.
📊
Key Findings & Data:We name them the curves $N-T^{\ast }B^{\ast }$.
💡
Conclusion & Impact:And we express the Frenet vectors and the curvatures of the curve $\beta^*$ in terms of the Frenet vectors and the curvatures of the curve $\beta$.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Frenet frame --- Curvatures --- Associated curves · Frenet frame --- Curvatures --- Associated curves · Frenet frame

Abstract

In this paper, we describe a new pair of curves where the principal normal vector of a curve $\beta$ and an vector $R^*$ lying in the rectifian plane of a curve $\beta^*$ are linearly dependent. We name them the curves $N-T^{\ast }B^{\ast }$. And we express the Frenet vectors and the curvatures of the curve $\beta^*$ in terms of the Frenet vectors and the curvatures of the curve $\beta$.

🔖

Cite This Article

Kılıçoglu, Ş., Şenyurt, S., Mazlum, S. G. (2022). The Frenet Vectors and the Curvatures of Curves $\mathit{{\mathbf{N-T^{\ast }B^{\ast }}}}$ in $\mathbf{E}^{3}$. Hagia Sophia Journal of Geometry, Cilt: 4 Sayı: 2, 11–18. https://ajindex.com/articles/906557

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