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Journals / International Electronic Journal of Geometry / 2021 / Cilt: 14 - Sayı: 1

Canal Surface Whose Center Curve is a Hyperbolic Curve with Hyperbolic Frame

Ali UÇUM
Pages
106–120
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

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

Lastly, we give the geometric properties of thesesurfaces such that Weingarten surface, $\left( X,Y\right) $-Weingarten surface and linear Weingarten surface.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we obtain the parametrization of the canal surfaces whose center curves are the hyperbolic curves on the hyperbolic space $H^{2}$ in $%\mathbb{E}_{1}^{3}$.
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Key Findings & Data:The parametrization of the canal surface is expressed according to the hyperbolic frame given in [10].
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Conclusion & Impact:Lastly, we give the geometric properties of thesesurfaces such that Weingarten surface, $\left( X,Y\right) $-Weingarten surface and linear Weingarten surface.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Canal surfaces · tubular surfaces · hyperbolic curve

Abstract

In this paper, we obtain the parametrization of the canal surfaces whose center curves are the hyperbolic curves on the hyperbolic space $H^{2}$ in $%\mathbb{E}_{1}^{3}$. The parametrization of the canal surface is expressed according to the hyperbolic frame given in [10]. Then, the parallelsurface of this surface is studied. Also, we define the notion of the associated canal surface. Lastly, we give the geometric properties of thesesurfaces such that Weingarten surface, $\left( X,Y\right) $-Weingarten surface and linear Weingarten surface.

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Cite This Article

UÇUM, A. (2022). Canal Surface Whose Center Curve is a Hyperbolic Curve with Hyperbolic Frame. International Electronic Journal of Geometry, Cilt: 14 - Sayı: 1, 106–120. https://ajindex.com/articles/539568

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