  The large N limit of the 3-d Gross-Neveu model is here studied on manifolds
with positive and negative constant curvature. Using the $\zeta$-function
regularization we analyze the critical properties of this model on the spaces
$S^2 \times S^1$ and $H^2\times S^1$. We evaluate the free energy density, the
spontaneous magnetization and the correlation length at the ultraviolet fixed
point. The limit $S^1\to R$, which is interpreted as the zero temperature
limit, is also studied.
