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

Authors : Uğur DURSUN, Güler Gürpınar ARSAN

Pages : 617-625

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Publication Date : 2011-05-01

Article Type : Research Paper

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.
Keywords : Minimal surface, Normal bundle, Mean curvature, Pointwise 1 type, Gauss map