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A classification of Monge-Ampère equations. (English) Zbl 0789.58078
Local classification of a class of Monge-Ampère equations on smooth manifolds is studied. The authors use the method of differential forms and contact geometry on first order jet bundles. In the case of 2 dimensions the reduction of the nonlinear Monge-Ampère equation to a quasi linear one and normal forms are shown. Most of the paper is devoted to problems of algebraic reduction in higher dimensions via invariant theory. For three dimensions \(C\)-infinity classification is obtained and for higher dimension partial results are presented.
Reviewer: C.Günther (Libby)

MSC:
58J70 Invariance and symmetry properties for PDEs on manifolds
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
58A10 Differential forms in global analysis
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