  We study the finite size effects on Bose-Einstein condensation (BEC) of an
ideal non-relativistic Bose gas in the three-sphere (spatial section of the
Einstein universe) and in a partially finite box which is infinite in two of
the spatial directions (infinite slab). Using the framework of grand-canonical
statistics, we consider the number of particles, the condensate fraction and
the specific heat. After obtaining asymptotic expansions for large system size,
which are valid throughout the BEC regime, we describe analytically how the
thermodynamic limit behaviour is approached. In particular, in the critical
region of the BEC transition, we express the chemical potential and the
specific heat as simple explicit functions of the temperature, highlighting the
effects of finite size. These effects are seen to be different for the two
different geometries. We also consider the Bose gas in a one-dimensional box, a
system which does not possess BEC in the sense of a phase transition even in
the infinite volume limit.
