Journal of Applied Mathematics
Volume 2013 (2013), Article ID 757041, 8 pages
http://dx.doi.org/10.1155/2013/757041
Research Article

On Complete Spacelike Hypersurfaces in a Semi-Riemannian Warped Product

Yaning Wang1 and Ximin Liu2

1Department of Mathematics, South China University of Technology, Guangzhou, Guangdong 510641, China
2School of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning 116024, China

Received 19 November 2012; Revised 26 January 2013; Accepted 26 January 2013

Academic Editor: P. G. L. Leach

Copyright © 2013 Yaning Wang and Ximin Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

By applying Omori-Yau maximal principal theory and supposing an appropriate restriction on the norm of gradient of height function, we obtain some new Bernstein-type theorems for complete spacelike hypersurfaces with nonpositive constant mean curvature immersed in a semi-Riemannian warped product. Furthermore, some applications of our main theorems for entire vertical graphs in Robertson-Walker spacetime and for hypersurfaces in hyperbolic space are given.