We investigate the gauged NJL-model in curved space-time using the RG
formulation and the equivalency with the gauge Higgs-Yukawa model in a
modified 1/N-c expansion. The strong curvature induced chiral symmetr
y breaking is found in the non-perturbative RG approach (presumably eq
uivalent to the ladder Schwinger-Dyson equations). The dynamically gen
erated fermion mass is explicitly calculated and inducing of Einstein
gravity is briefly discussed, This approach shows the way to the non-p
erturbative study of the dynamical symmetry breaking at external field
s.