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Journals / International Electronic Journal of Geometry / 2026 / Volume: 14 Issue: 1

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

Ali Uçum(KIRIKKALE UNİVERSİTY)0000-0003-0172-1531
Pages
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Publication Date
2021-04-15
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AI Summary & Key Takeaways

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

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

📌 3 Key Takeaways

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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 these surfaces 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 parallel surface of this surface is studied. Also, we define the notion of the associated canal surface. Lastly, we give the geometric properties of these surfaces such that Weingarten surface, $\left( X,Y\right) $-Weingarten surface and linear Weingarten surface.

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Cite This Article

Uçum, A. (2021). Canal Surface Whose Center Curve is a Hyperbolic Curve with Hyperbolic Frame. International Electronic Journal of Geometry, Volume: 14 Issue: 1. https://doi.org/10.36890/iejg.829766

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