  Experimental data on thin films of cylinder-forming block copolymers (BC) --
free-standing BC membranes as well as supported BC films -- strongly suggest
that the local orientation of the BC patterns is coupled to the geometry in
which the patterns are embedded. We analyze this phenomenon using general
symmetry considerations and numerical self-consistent field studies of curved
BC films in cylindrical geometry. The stability of the films against
curvature-induced dewetting is also analyzed. In good agreement with
experiments, we find that the BC cylinders tend to align along the direction of
curvature at high curvatures. At low curvatures, we identify a transition from
perpendicular to parallel alignment in supported films, which is absent in free
standing membranes. Hence both experiments and theory show that curvature can
be used to manipulate and align BC patterns.
