  Induced quantum gravity dynamics built over a Riemann surface is studied in
arbitrary dimension. Local coordinates on the target space are given by means
of the Laguerre-Forsyth construction. A simple model is proposed and
pertubatively quantized. In doing so, the classical W-symmetry turns out to be
preserved on-shell at any order of the $\hbar$ perturbative expansion. As a
main result, due to quantum corrections, the target coordinates acquire a
non-trivial character.
