Classification of surfaces in a pseudo-sphere with 2-type pseudo-spherical Gauss map

Burcu Bektaş*, Elif Özkara Canfes, Uğur Dursun

*Bu çalışma için yazışmadan sorumlu yazar

Araştırma sonucu: ???type-name???Makalebilirkişi

4 Atıf (Scopus)

Özet

In this article, we study submanifolds in a pseudo-sphere with 2-type pseudo-spherical Gauss map. We give a characterization theorem for Lorentzian surfaces in the pseudo-sphere S4 2 ⊂ E5 2 with zero mean curvature vector in S4 2 and 2-type pseudo-spherical Gauss map. We also prove that non-totally umbilical proper pseudo-Riemannian hypersurfaces in a pseudo-sphere Sn+1 s ⊂ En+2 s with non-zero constant mean curvature has 2-type pseudo-spherical Gauss map if and only if it has constant scalar curvature. Then, for n=2 we obtain the classification of surfaces in S3 1 ⊂ E4 1 with 2-type pseudo-spherical Gauss map. Finally, we give an example of surface with null 2-type pseudo-spherical Gauss map which does not appear in Riemannian case, and we give a characterization theorem for Lorentzian surfaces in S3 1 ⊂ E4 1 with null 2-type pseudo-spherical Gauss map.

Orijinal dilİngilizce
Sayfa (başlangıç-bitiş)2512-2523
Sayfa sayısı12
DergiMathematische Nachrichten
Hacim290
Basın numarası16
DOI'lar
Yayın durumuYayınlandı - Kas 2017

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Publisher Copyright:
© 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

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