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Almost product structures and Monge-Ampère equations. (English) Zbl 1116.35003
This paper is devoted to the equivalence problem of classical Monge-Ampère equations. At first, the author investigates tensor differential invariants of almost product structures. Then the obtained technique is applied to elliptic and hyperbolic Monge-Ampère equations. Namely, the author finds sufficient conditions for the contact linearization of these equations. Furthermore he reduces the equivalence problem of generic equations of the considered types to the equivalence problem of the corresponding complete parallelisms.

MSC:
35A30 Geometric theory, characteristics, transformations in context of PDEs
35J60 Nonlinear elliptic equations
35L70 Second-order nonlinear hyperbolic equations
58J05 Elliptic equations on manifolds, general theory
58J45 Hyperbolic equations on manifolds
58J70 Invariance and symmetry properties for PDEs on manifolds
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