ORIGINAL PAPER

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

Corresponding Author

Burcu Bektaş

[email protected]

Faculty of Science and Letters, Department of Mathematics, Istanbul Technical University, Maslak, 34469 Istanbul, Turkey

Correspondence

Burcu Bektaş, Faculty of Science and Letters, Department of Mathematics, Istanbul Technical University, Maslak, 34469, Istanbul, Turkey.

Email: [email protected]

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Elif Özkara Canfes,

Elif Özkara Canfes

Faculty of Science and Letters, Department of Mathematics, Istanbul Technical University, Maslak, 34469 Istanbul, Turkey

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Uğur Dursun,

Uğur Dursun

Faculty of Arts and Science, Department of Mathematics, Işık University, Şile, 34980 Istanbul, Turkey

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Burcu Bektaş,

Corresponding Author

Burcu Bektaş

[email protected]

Faculty of Science and Letters, Department of Mathematics, Istanbul Technical University, Maslak, 34469 Istanbul, Turkey

Correspondence

Burcu Bektaş, Faculty of Science and Letters, Department of Mathematics, Istanbul Technical University, Maslak, 34469, Istanbul, Turkey.

Email: [email protected]

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Elif Özkara Canfes,

Elif Özkara Canfes

Faculty of Science and Letters, Department of Mathematics, Istanbul Technical University, Maslak, 34469 Istanbul, Turkey

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Uğur Dursun,

Uğur Dursun

Faculty of Arts and Science, Department of Mathematics, Işık University, Şile, 34980 Istanbul, Turkey

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First published: 19 June 2017

https://doi.org/10.1002/mana.201600498

Citations: 7

Funding Information: Istanbul Teknik Üniversitesi, Grant Number: 38386.

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Abstract

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 $urn:x-wiley:0025584X:media:mana201600498:mana201600498-math-0001$ with zero mean curvature vector in $urn:x-wiley:0025584X:media:mana201600498:mana201600498-math-0002$ and 2-type pseudo-spherical Gauss map. We also prove that non-totally umbilical proper pseudo-Riemannian hypersurfaces in a pseudo-sphere $urn:x-wiley:0025584X:media:mana201600498:mana201600498-math-0003$ with non-zero constant mean curvature has 2-type pseudo-spherical Gauss map if and only if it has constant scalar curvature. Then, for $urn:x-wiley:0025584X:media:mana201600498:mana201600498-math-0004$ we obtain the classification of surfaces in $urn:x-wiley:0025584X:media:mana201600498:mana201600498-math-0005$ 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 $urn:x-wiley:0025584X:media:mana201600498:mana201600498-math-0006$ with null 2-type pseudo-spherical Gauss map.

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