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Dergiler / 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
Sayfa
617–625
Yayın Tarihi
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 Maddede Bu Makale

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Amaç & Hipotez:In this article we study surfaces in Euclidean space $Bbb{E}^4$ with pointwise 1-type Gauss map.
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Temel Bulgular & Veri: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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Sonuç & Katkı: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.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

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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Bu Makaleye Atıf Yap

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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Kaynakça (17)

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