  We derive the effective dimensionally reduced Sch\"odinger equation for
electrons in strain-driven curved nanostructures by adiabatic separation of
fast and slow quantum degrees of freedom. The emergent strain-induced geometric
potential strongly renormalizes the purely quantum curvature-induced potential
and enhances the effects of curvature by several orders of magnitude. Applying
this analysis to nanocorrugated films shows that this curvature-induced
potential leads to strongly enhanced electron localization and the opening of
substantial band gaps.
