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LINEAR WEINGARTEN HYPERSURFACES WITH BOUNDED MEAN CURVATURE IN THE HYPERBOLIC SPACE

Part of: Global differential geometry

Published online by Cambridge University Press:  17 December 2014

CÍCERO P. AQUINO ,
HENRIQUE F. DE LIMA  and
MARCO ANTONIO L. VELÁSQUEZ
CÍCERO P. AQUINO
Affiliation:
Departamento de Matemática, Universidade Federal do Piauí, 64.049-550 Teresina, Piauí, Brazil E-mail: [email protected]
HENRIQUE F. DE LIMA
Affiliation:
Departamento de Matemática, Universidade Federal de Campina Grande, 58.429-970 Campina Grande, Paraíba, Brazil E-mail: [email protected]
MARCO ANTONIO L. VELÁSQUEZ
Affiliation:
Departamento de Matemática, Universidade Federal de Campina Grande, 58.429-970 Campina Grande, Paraíba, Brazil E-mail: [email protected]
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Abstract

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We apply appropriate maximum principles in order to obtain characterization results concerning complete linear Weingarten hypersurfaces with bounded mean curvature in the hyperbolic space. By supposing a suitable restriction on the norm of the traceless part of the second fundamental form, we show that such a hypersurface must be either totally umbilical or isometric to a hyperbolic cylinder, when its scalar curvature is positive, or to a spherical cylinder, when its scalar curvature is negative. Related to the compact case, we also establish a rigidity result.

MSC classification

Primary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.)
Secondary: 53C40: Global submanifolds
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 57 , Issue 3 , September 2015 , pp. 653 - 663
Copyright
Copyright © Glasgow Mathematical Journal Trust 2014 

References

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