  The phase behaviour and structural properties of a monolayer of hard
particles is examined in such a confinement, where the adsorbed particles are
constrained to the surface of a narrow hard cylindrical pore. The diameter of
the pore is chosen such that only first and second neighbour interactions occur
between the hard particles. The transfer operator method of Percus and Zhang
[Mol. Phys., 69, 347 (1990)] is reformulated to obtain information about the
structure of the monolayer. We have found that a true phase transition is not
possible in the examined range of pore diameters. The monolayer of hard spheres
undergoes a structural change from fluid-like order to a zigzag-like solid one
with increasing surface density. The case of hard cylinders is different in the
sense that a layering takes place continuously between a low density one-row
and a high density two-row monolayer. Our results reveal a clear discrepancy
with classical density functional theories, which do not distinguish
smectic-like ordering in bulk from that in narrow periodic pores.
