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Classification of surfaces in a pseudo‐sphere with 2‐type pseudo‐spherical Gauss map
Author(s) -
Bektaş Burcu,
Canfes Elif Özkara,
Dursun Uğur
Publication year - 2017
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201600498
Subject(s) - gauss map , mathematics , mean curvature , type (biology) , mathematical analysis , scalar curvature , gauss , gaussian curvature , surface (topology) , zero (linguistics) , curvature , constant (computer programming) , gauss–bonnet theorem , pure mathematics , geometry , mathematical physics , physics , einstein , ecology , linguistics , philosophy , quantum mechanics , biology , computer science , programming language
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‐sphereS 2 4 ⊂ E 2 5with zero mean curvature vector in S 2 4 and 2‐type pseudo‐spherical Gauss map. We also prove that non‐totally umbilical proper pseudo‐Riemannian hypersurfaces in a pseudo‐sphereS s n + 1 ⊂ E s n + 2with 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 inS 1 3 ⊂ E 1 4with 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 inS 1 3 ⊂ E 1 4with null 2‐type pseudo‐spherical Gauss map.