**DIPS 3/2008**[tex source, PostScript, PDF file, dvi]-
**Title:**Differential invariants of generic parabolic Monge-Ampere equations.**Authors:**D. Catalano Ferraioli and A. M. VinogradovSome 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.

24 pages, LaTeX-2e.

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