  We study the effects of the structural corrugation or rippling on the
electronic properties of undoped armchair graphene nanoribbons (AGNR). First,
reanalyzing the single corrugated graphene layer we find that the two
inequivalent Dirac points (DP), move away one from the other. Otherwise, the
Fermi velocity decrease by increasing rippling. Regarding the AGNRs, whose
metallic behavior depends on their width, we analyze in particular the case of
the zero gap band-structure AGNRs. By solving the Dirac equation with the
adequate boundary condition we show that due to the shifting of the DP a gap
opens in the spectra. This gap scale with the square of the rate between the
high and the wavelength of the deformation. We confirm this prediction by exact
numerical solution of the finite width rippled AGNR. Moreover, we find that the
quantum conductance, calculated by the non equilibrium Green's function
technique vanish when the gap open. The main conclusion of our results is that
a conductance gap should appear for all undoped corrugated AGNR independent of
their width.
