  The large N limit of the Gross-Neveu model is here studied on manifolds with
constant curvature, at zero and finite temperature. Using the zeta-function
regularization, the phase structure is investigated for arbitrary values of the
coupling constant. The critical surface where the second order phase transition
takes place is analytically found for both the positive and negative curvature
cases. For negative curvature, where the symmetry is always broken at zero
temperature, the mass gap is calculated. The free energy density is evaluated
at criticality and the zero curvature and zero temperature limits are
discussed.
