  The global geometries of bulk vacuum space-times in the brane-universe models
are investigated and classified in terms of geometrical invariants. The
corresponding Carter-Penrose diagrams and embedding diagrams are constructed.
It is shown that for a given energy-momentum induced on the brane there can be
different types of global geometries depending on the signs of a bulk
cosmological term and surface energy density of the brane (the sign of the
latter does not influence the internal cosmological evolution). It is shown
that in the Randall-Sundrum scenario it is possible to have an asymmetric
hierarchy splitting even with a $Z_2$-symmetric matching of "our" brane to the
bulk.
