{"paper":{"title":"Meta-Symplectic Geometry of $3^{\\rm rd}$ Order Monge-Amp\\`ere Equations and their Characteristics","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Gianni Manno, Giovanni Moreno","submitted_at":"2014-03-14T10:23:56Z","abstract_excerpt":"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 a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3521","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}