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CHARACTERIZATIONS OF LINEAR WEINGARTEN SPACELIKE HYPERSURFACES IN EINSTEIN SPACETIMES

Published online by Cambridge University Press:  25 February 2013

HENRIQUE F. DE LIMA and
JOSEÍLSON R. DE LIMA
HENRIQUE F. DE LIMA
Affiliation:
Departamento de Matemática e Estatística, Universidade Federal de Campina Grande, 58429-970 Campina Grande, Paraíba, Brazil e-mails: henrique@dme.ufcg.edu.br, joseilson@dme.ufcg.edu.br
JOSEÍLSON R. DE LIMA
Affiliation:
Departamento de Matemática e Estatística, Universidade Federal de Campina Grande, 58429-970 Campina Grande, Paraíba, Brazil e-mails: henrique@dme.ufcg.edu.br, joseilson@dme.ufcg.edu.br
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Abstract

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Our purpose is to study the geometry of linear Weingarten spacelike hypersurfaces immersed in a locally symmetric Einstein spacetime, whose sectional curvature is supposed to obey some standard restrictions. In this setting, by using as main analytical tool a generalized maximum principle for complete non-compact Riemannian manifolds, we establish sufficient conditions to guarantee that such a hypersurface must be either totally umbilical or an isoparametric hypersurface with two distinct principal curvatures, one of which is simple. Applications to the de Sitter space are given.

Keywords

Primary 53C42Secondary 53A1053B30 and 53C50

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 55 , Issue 3 , September 2013, pp. 567 - 579
Copyright
Copyright © Glasgow Mathematical Journal Trust 2013 

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