A Class of Complete Hypersurfaces Immersed in Semi-Riemannian Warped Product Spaces

We deal with complete hypersurfaces immersed in a semi-Riemannian warped product of the type eI×f M,where Mis a connected n-dimensional oriented Riemannian manifold.When the fiber Mis complete with sectional curvature-k≤Kfor 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.