Linear Weingarten hypersurfaces in locally symmetric manifolds

The complete linear Weingarten hypersurfaces with bounded mean curvature in locally symmetric manifold are studied. By supposing a suitable restriction on the norm of which is symmetric tensor in M^n, it is proved that such a hypersurface must be either totally umbilical or isometric to the hypersurface with two distinct principle curvatures, one of which is simple.