Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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G. Manno - G. Moreno

Meta-Symplectic Geometry of $3^{\rm rd}$ Order Monge-Ampère Equations and their Characteristics

created by moreno on 15 Sep 2020



Inserted: 15 sep 2020
Last Updated: 15 sep 2020

Year: 2014

ArXiv: 1403.3521 PDF


This paper is a natural companion of Alekseevsky D.V., Alonso Blanco R., Manno G., Pugliese F., Ann. Inst. Fourier (Grenoble) 62 (2012), 497-524, arXiv:1003.5177, generalising its perspectives and results to the context of third-order (2D) Monge-Amp\`ere equations, by using the so-called "meta-symplectic structure" associated with the 8D prolongation $M^{(1)}$ of a 5D contact manifold $M$. We write down a geometric definition of a third-order Monge-Amp\`ere equation in terms of a (class of) differential two-form on $M^{(1)}$. In particular, the equations corresponding to decomposable forms admit a simple description in terms of certain three-dimensional distributions, which are made from the characteristics of the original equations. We conclude the paper with a study of the intermediate integrals of these special Monge-Amp\`ere equations, herewith called of Goursat type.

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