Title of article
SURFACES IN THE EUCLIDEAN SPACE E4 WITH POINTWISE 1-TYPE GAUSS MAP
Author/Authors
Dursun, Ugur Istanbul Technical University - Faculty of Science and Letters - Department of Mathematics, Istanbul, Turkey , Gurpınar Arsan, Guler Istanbul Technical University - Faculty of Science and Letters - Department of Mathematics, Istanbul, Turkey
Pages
9
From page
617
To page
625
Abstract
In this article we study surfaces in Euclidean space E4 with pointwise 1-type Gauss map. We give a characterization of surfaces in E4 with a pointwise 1-type Gauss map of the first kind. We conclude that an oriented non-minimal surface M in E4 has a pointwise 1-type Gauss map of the first kind if and only if M is a surface in a 3-sphere of E4 with constant mean curvature. We also obtain a characterization for non-planar minimal surfaces in E4 with pointwise 1-type Gauss map of the second kind. Further we give a partial classification of surfaces in E4 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.
Journal title
Hacettepe Journal Of Mathematics and Statistics
Serial Year
2011
Journal title
Hacettepe Journal Of Mathematics and Statistics
Record number
2650995
Link To Document