This paper address the geometry of complete linear Weingarten spacelike hypersurfaces in the Lorentz space forms. First, a divergence lemma concerning linear Weingarten spacelike hypersurfaces is obtained. Then, with the aid of this lemma, by supposing suitable restrictions on the Gauss map, we show that such hypersurfaces must be totally umbilical, which are some extension of the recent results of Aquino, Bezerra and Lima  and Aquino, Lima and Velásquez .
"Linear Weingarten spacelike hypersurfaces in Lorentz space forms with prescribed Gauss map." Kodai Math. J. 41 (1) 98 - 114, March 2018. https://doi.org/10.2996/kmj/1521424826