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Journals / Hagia Sophia Journal of Geometry / 2023 / Cilt: 5 Sayı: 2

Directional Tube Surface in Euclidean 4-Space

Başak Yağbasan0000-0003-4067-3034
Cumali Ekici(ESKİŞEHİR OSMANGAZİ ÜNİVERSİTESİ)0000-0002-3247-5727
Hatice Tozak
Pages
18–30
Publication Date
2023-12-30
DOI
—
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AI Summary & Key Takeaways

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

Subsequently, an example of a directional tube surface is given in $\mathbb{E}^{4}$, together with visual representations of this tube surfaces in projection space.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The aim of this paper is to study characterization of tube surfaces (called directional tube surfaces) with respect to the q-frame in Euclidean $4$-space $\mathbb{E}^{4}$.
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Key Findings & Data:First, a parametrization of these directional tube surfaces in $\mathbb{E}^{4}$ is established.
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Conclusion & Impact:Subsequently, an example of a directional tube surface is given in $\mathbb{E}^{4}$, together with visual representations of this tube surfaces in projection space.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:quasi-frame · curvatures · Euclidean space

Abstract

The aim of this paper is to study characterization of tube surfaces (called directional tube surfaces) with respect to the q-frame in Euclidean $4$-space $\mathbb{E}^{4}$. First, a parametrization of these directional tube surfaces in $\mathbb{E}^{4}$ is established. Then, the normals of the directional tube surfaces, denoted as $\mathbf{U}_{1}$ and $\mathbf{U}_{2}$, are determined respectively. Furthermore, the Gaussian curvature $K$ and the mean curvature $H$ of the directional tube surfaces are investigated. Subsequently, an example of a directional tube surface is given in $\mathbb{E}^{4}$, together with visual representations of this tube surfaces in projection space.

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Cite This Article

Yağbasan, B., Ekici, C., Tozak, H. (2023). Directional Tube Surface in Euclidean 4-Space. Hagia Sophia Journal of Geometry, Cilt: 5 Sayı: 2, 18–30. https://ajindex.com/articles/1490435

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