[en] The large N limit of the Gross-Neveu model is here studied on manifolds with constant curvature, at zero and finite temperature. Using the ζ-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