  The study of gravitational waves in the presence of a cosmological constant
has led to interesting forms of the de Sitter and anti-de Sitter line elements
based on families of null hypersurfaces. The forms are interesting because they
focus attention on the geometry of null hypersurfaces in space-times of
constant curvature. Two examples are worked out in some detail. The first
originated in the study of collisions of impulsive gravitational waves in which
the post-collision space-time is a solution of Einstein's field equations with
a cosmological constant, and the second originated in the generalisation of
plane fronted gravitational waves with parallel rays to include a cosmological
constant.
