  We carry out the spatially periodic homogenization of nonlinear bending
theory for plates. The derivation is rigorous in the sense of
Gamma-convergence. In contrast to what one naturally would expect, our result
shows that the limiting functional is not simply a quadratic functional of the
second fundamental form of the deformed plate as it is the case in nonlinear
plate theory. It turns out that the limiting functional discriminates between
whether the deformed plate is locally shaped like a "cylinder" or not. For the
derivation we investigate the oscillatory behavior of sequences of second
fundamental forms associated with isometric immersions, using two-scale
convergence. This is a non-trivial task, since one has to treat two-scale
convergence in connection with a nonlinear differential constraint.
