Complete Linear Weingarten Spacelike Hypersurfaces Immersed in a Locally Symmetric Lorentz Space

In this paper, we establish a characterization theorem concerning the complete linear Weingarten spacelike hypersurfaces immersed in a locally symmetric Lorentz space, whose sectional curvature is supposed to obey certain appropriated conditions. Under a suitable restriction on the length of the second fundamental form, we prove that a such spacelike hypersurface must be either totally umbilical or an isoparametric hypersurface with two distinct principal curvatures one of which is simple.