Authors:D. Catalano Ferraioli and A. M. Vinogradov

Some new results on geometry of classical parabolic Monge-Ampere equations (PMA) are presented. PMAs are either integrable, or nonintegrable according to integrability of its characteristic distribution. All integrable PMAs are locally equivalent to the equation u_xx=0. We study nonintegrable PMAs by associating with each of them a 1-dimensional distribution on the corresponding first order jet manifold, called the directing distribution. According to some property of these distributions, nonintegrable PMAs are subdivided into three classes, one generic and two special ones. Generic PMAs are uniquely characterized by their directing distributions. To study directing distributions we introduce their canonical models, projective curve bundles (PCB). A PCB is a 1-dimensional subbundle of the projectivized cotangent bundle to a 4-dimensional manifold. Differential invariants of projective curves composing such a bundle are used to construct a series of contact differential invariants for corresponding PMAs. These give a solution of the equivalence problem for PMAs with respect to contact transformations.

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