  String propagation on D-dimensional curved backgrounds with Lorentzian
signature is formulated as a geometrical problem of embedding surfaces. When
the spatial part of the background corresponds to a general WZW model for a
compact group, the classical dynamics of the physical degrees of freedom is
governed by the coset conformal field theory SO(D-1)/SO(D-2), which is
universal irrespective of the particular WZW model. The same holds for string
propagation on D-dimensional flat space. The integration of the corresponding
Gauss-Codazzi equations requires the introduction of (non-Abelian) parafermions
in differential geometry.
