  A new framework is found for the compactification of supersymmetric string
theory. It is shown that the massless spectra of Calabi--Yau manifolds of
complex dimension $D_{crit}$ can be derived from noncritical manifolds of
complex dimension $2k + D_{crit}$, $k\geq 1$. These higher dimensional
manifolds are spaces whose nonzero Ricci curvature is quantized in a particular
way. This class is more general than that of Calabi--Yau manifolds because it
contains spaces which correspond to critical string vacua with no K\"ahler
deformations, i.e. no antigenerations, thus providing mirrors of rigid
Calabi--Yau manifolds. The constructions introduced here lead to new insights
into the relation between exactly solvable models and their mean field theories
on the one hand and Calabi--Yau manifolds on the other. They also raise
fundamental questions about the Kaluza--Klein concept of string
compactification, in particular regarding the r\^{o}le played by the dimension
of the internal theories.
