  Coulomb systems in which the particles interact through the $d$-dimensional
Coulomb potential but are confined in a flat manifold of dimension $d - 1$ are
considered. The Coulomb potential is defined with some boundary condition
involving a characteristic macroscopic distance $W$ in the direction
perpendicular to the manifold~: either it is periodic of period $W$ in that
direction, or it vanishes on one ideal conductor wall parallel to the manifold
at a distance $W$ from it, or it vanishes on two parallel walls at a distance
$W$ from each other with the manifold equidistant from them. Under the
assumptions that classical equilibrium statistical mechanics is applicable and
that the system has the macroscopic properties of a conductor, it is shown that
the suitably smoothed charge correlation function is universal, and that the
free energy and the grand potential have universal dependences on $W$
(universal means independent of the microscopic detail). The cases $d = 2$ are
discussed in detail, and the generic results are checked on an exactly solvable
model. The case $d = 3$ of a plane parallel to an ideal conductor is also
explicitly worked out.
