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Journals / Hacettepe Journal of Mathematics and Statistics / 2011 / Cilt: 40 - Sayı: 5

Surfaces in the Euclidean space $Bbb{E}^4$ with pointwise 1-type Gauss map

Uğur DURSUN
GÜRPINAR Güler ARSAN
Pages
617–625
Publication Date
2022-10-18
DOI
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Further we give a partial classification of surfaces in $Bbb{E}^4$ in terms of the pointwise 1-type Gauss map of the second kind.

📌 3 Key Takeaways

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Objective & Hypothesis:In this article we study surfaces in Euclidean space $Bbb{E}^4$ with pointwise 1-type Gauss map.
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Key Findings & Data:We give a characterization of surfaces in $Bbb{E}^4$ with a pointwise 1-type Gauss map of the first kind.
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Conclusion & Impact:Further we give a partial classification of surfaces in $Bbb{E}^4$ in terms of the pointwise 1-type Gauss map of the second kind.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this article we study surfaces in Euclidean space $Bbb{E}^4$ with pointwise 1-type Gauss map. We give a characterization of surfaces in $Bbb{E}^4$ with a pointwise 1-type Gauss map of the first kind. We conclude that an oriented non-minimal surface M in $Bbb{E}^4$ has a pointwise 1-type Gauss map of the first kind if and only if M is a surface in a 3-sphere of $Bbb{E}^4$ with constant mean curvature. We also obtain a characterization for non-planar minimal surfaces in $Bbb{E}^4$ with pointwise 1-type Gauss map of the second kind. Further we give a partial classification of surfaces in $Bbb{E}^4$ in terms of the pointwise 1-type Gauss map of the second kind.

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Cite This Article

DURSUN, U., ARSAN, G. G. (2022). Surfaces in the Euclidean space $Bbb{E}^4$ with pointwise 1-type Gauss map. Hacettepe Journal of Mathematics and Statistics, Cilt: 40 - Sayı: 5, 617–625. https://ajindex.com/articles/530577

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