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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Bernstein-type theorems in semi-Riemannian warped products


Authors: F. Camargo, A. Caminha and H. de Lima
Journal: Proc. Amer. Math. Soc. 139 (2011), 1841-1850
MSC (2010): Primary 53C42; Secondary 53B30, 53C50, 53Z05, 83C99
Published electronically: October 8, 2010
MathSciNet review: 2763771
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Abstract: This paper deals with complete hypersurfaces immersed in the $ (n+1)$-dimensional hyperbolic and steady state spaces. By applying a technique of S. T. Yau and imposing suitable conditions on both the $ r$-th mean curvatures and on the norm of the gradient of the height function, we obtain Bernstein-type results in each of these ambient spaces.


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Additional Information

F. Camargo
Affiliation: Departamento de Matemática e Estatística, Universidade Federal de Campina Grande, Campina Grande, Paraíba, Brazil 58109-970
Email: fernandaecc@dme.ufcg.edu.br

A. Caminha
Affiliation: Departamento de Matemática, Universidade Federal do Ceará, Fortaleza, Ceará, Brazil 60455-760
Email: antonio.caminha@gmail.com

H. de Lima
Affiliation: Departamento de Matemática e Estatística, Universidade Federal de Campina Grande, Campina Grande, Paraíba, Brazil 58109-970
Email: henrique@dme.ufcg.edu.br

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10597-X
PII: S 0002-9939(2010)10597-X
Keywords: Semi-Riemannian manifolds, Lorentz geometry, hyperbolic space, steady state space, spacelike hypersurfaces, mean curvature, Bernstein-type theorems
Received by editor(s): November 6, 2009
Received by editor(s) in revised form: March 29, 2010, and May 18, 2010
Published electronically: October 8, 2010
Additional Notes: The second author is partially supported by CNPq
The third author is partially supported by PPP/FAPESQ/CNPq
Communicated by: Richard A. Wentworth
Article copyright: © Copyright 2010 American Mathematical Society