  We study constant mean curvature spacelike hypersurfaces and in particular
maximal hypersurfaces immersed in pp-wave spacetimes satisfying the timelike
convergence condition. We prove the non-existence of compact spacelike
hypersurfaces whose constant mean curvature is non-zero and also that every
compact maximal hypersurface is totally geodesic. Moreover, we give an
extension of the classical Calabi-Bernstein theorem to this class of pp-wave
spacetimes.
