  A continuum mechanical framework is developed for determining a) the class of
stress-free deformed shapes and corresponding director distributions on the
undeformed configuration of a nematic glass membrane that has a prescribed
spontaneous stretch field and b) the class of undeformed configurations and
corresponding director distributions on it resulting in a stress-free
\emph{given} deformed shape of a nematic glass sheet with a prescribed
spontaneous stretch field. The proposed solution rests on an understanding of
how the Lagrangian dyad of a deformation of a membrane maps into the Eulerian
dyad in three dimensional ambient space. Interesting connections between these
practical questions of design and the mathematical theory of isometric
embeddings of manifolds, deformations between two prescribed Riemannian
manifolds, and the slip-line theory of plasticity are pointed out.
