Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

We give some characterizations of n dimensional (n leg 2) hyperbolic cylinder, spherical cylinder or Euclidean cylinder in a Lorentzian space form. We show that the hyperbolic cylinder, spherical cylinder or Euclidean cylinder is the only complete spacelike hypersurface in an (n+1) dimensional Lorentzian space form Mn+1 1 (c) with non-zero constant mean curvature and two distinct principal curvatures one of which is simple, if the norm square of the second fundamental form of Mn satisfies some pinching conditions, respectively.