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2011•DergiPark (Istanbul University)Open access

Surfaces in the Euclidean Space E4 with Pointwise 1-Type Gauss Map

Uğur Dursun, Güler Gürpınar Arsan

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Abstract

In this article we study surfaces in Euclidean space E 4 with pointwise 1-type Gauss map.We give a characterization of surfaces in E 4 with a pointwise 1-type Gauss map of the first kind.We conclude that an oriented non-minimal surface M in 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 E 4 with constant mean curvature.We also obtain a characterization for non-planar minimal surfaces in E 4 with pointwise 1-type Gauss map of the second kind.Further we give a partial classification of surfaces in E 4 in terms of the pointwise 1-type Gauss map of the second kind.

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In this article we study surfaces in Euclidean space E 4 with pointwise 1-type Gauss map.We give a characterization of surfaces in E 4 with a pointwise 1-type Gauss map of the first kind.We conclude that an oriented non-minimal surface M in 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 E 4 with constant mean curvature.We also obtain a characterization for non-planar minimal surfaces in E 4 with pointwise 1-type Gauss map of the second kind.Further we give a partial classification of surfaces in E 4 in terms of the pointwise 1-type Gauss map of the second kind.

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Available abstract

In this article we study surfaces in Euclidean space E 4 with pointwise 1-type Gauss map.We give a characterization of surfaces in E 4 with a pointwise 1-type Gauss map of the first kind.We conclude that an oriented non-minimal surface M in 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 E 4 with constant mean curvature.We also obtain a characterization for non-planar minimal surfaces in E 4 with pointwise 1-type Gauss map of the second kind.Further we give a partial classification of surfaces in E 4 in terms of the pointwise 1-type Gauss map of the second kind.

Key concepts: Pointwise, Gauss map, Mathematics, Type (biology), Characterization (materials science), Gauss, Mean curvature, Euclidean space

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