Normal forms for parabolic Monge-Ampere equations

Details Normal forms for parabolic Monge-Ampere equations Normal forms for parabolic Monge-Ampere equations

2007-07-04

arxiv.org/abs/0707.0683v3

Mathematics

Differential Geometry

18 pages

Scientific paper

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).

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