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

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,

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