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SOME CLASSIFICATIONS OF LORENTZIAN SURFACES WITH FINITE TYPE GAUSS MAP IN THE MINKOWSKI 4-SPACE

Part of: Global differential geometry Classical differential geometry Local differential geometry

Published online by Cambridge University Press:  13 August 2015

NURETTIN CENK TURGAY
NURETTIN CENK TURGAY*
Affiliation:
Istanbul Technical University, Faculty of Science and Letters, Department of Mathematics, 34469 Maslak, Istanbul, Turkey email turgayn@itu.edu.tr
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Abstract

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In this paper we study the Lorentzian surfaces with finite type Gauss map in the four-dimensional Minkowski space. First, we obtain the complete classification of minimal surfaces with pointwise 1-type Gauss map. Then, we get a classification of Lorentzian surfaces with nonzero constant mean curvature and of finite type Gauss map. We also give some explicit examples.

Keywords

Minkowski space–timeLorentzian surfacesconstant mean curvaturefinite type mappingspointwise 1-type Gauss map

MSC classification

Primary: 53A35: Non-Euclidean differential geometry
Secondary: 53B25: Local submanifolds 53C50: Lorentz manifolds, manifolds with indefinite metrics
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 99 , Issue 3 , December 2015 , pp. 415 - 427
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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