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April, 2014 Complete linear Weingarten hypersurfaces immersed in the hyperbolic space
Henrique Fernandes DE LIMA
J. Math. Soc. Japan 66(2): 415-423 (April, 2014). DOI: 10.2969/jmsj/06620415

Abstract

In this paper, we apply the Hopf's strong maximum principle in order to obtain a suitable characterization of the complete linear Weingarten hypersurfaces immersed in the hyperbolic space $\mathbb H^{n+1}$. Under the assumption that the mean curvature attains its maximum and supposing an appropriated restriction on the norm of the second fundamental form, we prove that such a hypersurface must be either totally umbilical or isometric to a hyperbolic cylinder of $\mathbb H^{n+1}$.

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Henrique Fernandes DE LIMA. "Complete linear Weingarten hypersurfaces immersed in the hyperbolic space." J. Math. Soc. Japan 66 (2) 415 - 423, April, 2014. https://doi.org/10.2969/jmsj/06620415

Information

Published: April, 2014
First available in Project Euclid: 23 April 2014

zbMATH: 1303.53080
MathSciNet: MR3201819
Digital Object Identifier: 10.2969/jmsj/06620415

Subjects:
Primary: 53C42
Secondary: 53A10 , 53C20 , 53C50

Keywords: hyperbolic cylinders , Hyperbolic space , Linear Weingarten hypersurfaces , Totally umbilical hypersurfaces

Rights: Copyright © 2014 Mathematical Society of Japan

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Vol.66 • No. 2 • April, 2014
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