  Some of the most important classes of surfaces in projective 3-space are
reviewed: these are isothermally asymptotic surfaces, projectively applicable
surfaces, surfaces of Jonas, projectively minimal surfaces, etc. It is
demonstrated that the corresponding projective "Gauss-Codazzi" equations reduce
to integrable systems which are quite familiar from the modern soliton theory
and coincide with the stationary flows in the Davey-Stewartson and
Kadomtsev-Petviashvili hierarchies, equations of the Toda lattice, etc. The
corresponding Lax pairs can be obtained by inserting a spectral parameter in
the equations of the Wilczynski moving frame.
