Uniqueness of complete spacelike hypersurface in Lorentzian warped products

In this paper, we apply several forms of generalized maximum principles to study the uniqueness of complete spacelike hypersurfaces immersed in Lorentzian warped products. First, we consider the cases of ambient space with vanish f', then obtain some uniqueness results of constant k-th mean curvature. Afterwards, we obtain the sign relationship between the support function with the derivative of warping function. By using this result, under some suitable restriction on the higher order mean curvature, we establish the uniqueness results of Lorentzian warped product -R x (f) M-n with non-vanish f'. Furthermore, applications to such spaces are given.