  We conpare predictions of the mean-field theory of supercnductivity for
metallic systems on the border of a density instability for cubic and
tetragonal lattices. The calculations are based on a parametrisation of an
effective interaction arising from the exchange of density fluctuations and
assume that a single band is relevant for superconductivity. The results show
that for comparable model parameters, desnity fluctuation mediated pairing is
more robust in quasi-two dimensions than in three dimensions, and that the
robustness of pairing increases gradually as one goes from a cubic to a more
and more anisotropic tetragonal structure. We also find that the robustness of
density fluctuation mediated pairing can depend sensitively on the incipient
ordering wavevector. We discuss the similarities and differences between the
mean-field theories of superconductivity for density and magnetically mediated
pairing.
