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Journals / Turkish Journal of Mathematics / 2012 / Cilt: 36 - Sayı: 4

Flat surfaces in the Minkowski space $Bbb{E}_{1}^{3}$ with pointwise 1-type Gauss map

Emel ÇOŞKUN
UĞUR DURSUN
Pages
613–629
Publication Date
2022-11-05
DOI
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AI Summary & Key Takeaways

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

We conclude that there is notangent developable surface fully lying in $Bbb{E}_{1}^{3}$ with pointwise 1-type Gauss map of the second kind.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this article, we obtain all nonplanar cylindrical surfaces in the Minkowski space $Bbb{E}_{1}^{3}$ with pointwise 1-type Gauss map of the second kind.
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Key Findings & Data:We also prove that right circular cones and hyperbolic cones in $Bbb{E}_{1}^{3}$ are the only cones in $Bbb{E}_{1}^{3}$ with pointwise 1-type Gauss map of the second kind.
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Conclusion & Impact:We conclude that there is notangent developable surface fully lying in $Bbb{E}_{1}^{3}$ with pointwise 1-type Gauss map of the second kind.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this article, we obtain all nonplanar cylindrical surfaces in the Minkowski space $Bbb{E}_{1}^{3}$ with pointwise 1-type Gauss map of the second kind. We also prove that right circular cones and hyperbolic cones in $Bbb{E}_{1}^{3}$ are the only cones in $Bbb{E}_{1}^{3}$ with pointwise 1-type Gauss map of the second kind. We conclude that there is notangent developable surface fully lying in $Bbb{E}_{1}^{3}$ with pointwise 1-type Gauss map of the second kind.

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Cite This Article

ÇOŞKUN, E., DURSUN, U. (2022). Flat surfaces in the Minkowski space $Bbb{E}_{1}^{3}$ with pointwise 1-type Gauss map. Turkish Journal of Mathematics, Cilt: 36 - Sayı: 4, 613–629. https://ajindex.com/articles/608413

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