  It is shown that a spacetime with collisionless matter evolving from data on
a compact Cauchy surface with hyperbolic symmetry can be globally covered by
compact hypersurfaces on which the mean curvature is constant and by compact
hypersurfaces on which the area radius is constant. Results for the related
cases of spherical and plane symmetry are reviewed and extended. The prospects
of using the global time coordinates obtained in this way to investigate the
global geometry of the spacetimes concerned are discussed.
