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 uxx=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
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