  Neveu-Schwarz-Ramond type heterotic and type-II superstrings in four
dimensional curved space-time are constructed as exact $N=1$ superconformal
theories. The tachyon is eliminated with a GSO projection. The theory is based
on the N=1 superconformal gauged WZW model for the anti-de Sitter coset
$SO(3,2)/SO(3,1)$ with integer central extension $k=5$. The model has dynamical
duality properties in its space-time metric that are similar to the large-small
($R\rightarrow 1/R$) duality of tori. To first order in a $1/k$ expansion we
give expressions for the metric, the dilaton, the Ricci tensor and their dual
generalizations. The curvature scalar has several singularities at various
locations in the 4-dimensional manifold. This provides a new singular solution
to Einstein's equations in the presence of matter in four dimensions. A
non-trivial path integral measure which we conjectured in previous work for
gauged WZW models is verified.
