  We consider a prototypical "stretching plus bending" functional of an elastic
shell. The shell is modeled as a d-dimensional Riemannian manifold endowed, in
addition to the metric, with a reference second fundamental form. The shell is
immersed into a (d+1)-dimensional ambient space, and the elastic energy
accounts for deviations of the induced metric and second fundamental forms from
their reference values. Under the assumption that the ambient space is of
constant sectional curvature, we prove that any sequence of immersions of
asymptotically vanishing energy converges to an isometric immersion of the
shell into ambient space, having the reference second fundamental form. In
particular, if the ambient space is Euclidean space, then the reference metric
and second fundamental form satisfy the Gauss-Codazzi-Mainardi compatibility
conditions. This theorem can be viewed as a (manifold-valued) co-dimension 1
analog of Reshetnyak's asymptotic rigidity theorem. It also relates to recent
results on the continuity of surfaces with respect to their fundamental forms.
