Surfaces in a pseudo-sphere with harmonic or 1-type pseudo-spherical Gauss map

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Bektaş B., Van der Veken J., Vrancken L.

ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, vol.52, no.1, pp.45-55, 2017 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 52 Issue: 1
• Publication Date: 2017
• Doi Number: 10.1007/s10455-017-9548-2
• Journal Name: ANNALS OF GLOBAL ANALYSIS AND GEOMETRY
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Page Numbers: pp.45-55
• Istanbul Technical University Affiliated: Yes

Abstract

We give a complete classification of Riemannian and Lorentzian surfaces of arbitrary codimension in a pseudo-sphere whose pseudo-spherical Gauss maps are of 1-type or, in particular, harmonic. In some cases a concrete global classification is obtained, while in other cases the solutions are described by an explicit system of partial differential equations.