  We find normal forms for parabolic Monge-Ampere equations. Of these, the most
general one holds for any equation admitting a complete integral. Moreover, we
explicitly give the determining equation for such integrals; restricted to the
analytic case, this equation is shown to have solutions. The other normal forms
exhaust the different classes of parabolic Monge-Ampere equations with symmetry
properties, namely, the existence of classical or nonholonomic intermediate
integrals. Our approach is based on the equivalence between parabolic
Monge-Ampere equations and particular distributions on a contact manifold, and
involves a classification of vector fields lying in the contact structure.
These are divided into three types and described in terms of the simplest ones
(characteristic fields of first order PDE's).
