Bernstein-type theorems in semi-Riemannian warped products

Camargo, F.; Caminha, A.; de Lima, H.

doi:10.1090/S0002-9939-2010-10597-X

Bernstein-type theorems in semi-Riemannian warped products
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by F. Camargo, A. Caminha and H. de Lima

Proc. Amer. Math. Soc. 139 (2011), 1841-1850

DOI: https://doi.org/10.1090/S0002-9939-2010-10597-X

Published electronically: October 8, 2010

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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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