A Class of Complete Hypersurfaces Immersed in Semi-Riemannian Warped Product Spaces
Received:October 19, 2015  Revised:March 09, 2016
Key Words: semi-Riemannian manifold   warped product   complete hypersurface   height function
Fund Project:Supported by the National Natural Science Foundation of China (Nos.11371076; 11431009).
 Author Name Affiliation Yan ZHAO School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China Ximin LIU School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China
Hits: 1952
We deal with complete hypersurfaces immersed in a semi-Riemannian warped product of the type $\epsilon\textit{I}\times _{f}M^{n}$, where $M^{n}$ is a connected $n$-dimensional oriented Riemannian manifold. When the fiber $M^{n}$ is complete with sectional curvature $-k\leq K_{M}$ for some positive constant $k$, under appropriate restrictions on the norm of the gradient of the height function $h$, we proceed with our technique in order to guarantee that complete hypersurface immersed in a semi-Riemannian warped product is a slice. Our approach is based on the well known generalized maximum principle and another suitable maximum principle at the infinity due to Yau.