Contact geometry of multidimensional Monge-Ampère equations: characteristics, intermediate integrals and solutions

DOI10.5802/aif.2686zbMath1253.53075arXiv1003.5177OpenAlexW1668002422MaRDI QIDQ441304

Fabrizio Pugliese, Gianni Manno, Dimitrii V. Alekseevsky, Ricardo J. Alonso-Blanco

Publication date: 22 August 2012

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1003.5177

zbMATH Keywords

contact geometrycharacteristicsMonge-Ampère equationshypersurfaces of Lagrangian Grassmanniansintermediate integralssubdistribution of a contact distribution

Mathematics Subject Classification ID

Pfaffian systems (58A17) Contact manifolds (general theory) (53D10) Geometric theory, characteristics, transformations in context of PDEs (35A30) Vector distributions (subbundles of the tangent bundles) (58A30)

Related Items (11)

Meta-symplectic geometry of \(3^{\mathrm{rd}}\) order Monge-Ampère equations and their characteristics ⋮ Finding solutions of parabolic Monge-Ampère equations by using the geometry of sections of the contact distribution ⋮ Monge-Ampère equations on (para-)Kähler manifolds: from characteristic subspaces to special Lagrangian submanifolds ⋮ Partial extensions of jets and the polar distribution on Grassmannians of non-maximal integral elements ⋮ The moment map on the space of symplectic 3D Monge-Ampère equations ⋮ Lowest degree invariant second-order PDEs over rational homogeneous contact manifolds ⋮ An introduction to completely exceptional second order scalar partial differential equations ⋮ Contact manifolds, Lagrangian Grassmannians and PDEs ⋮ Completely exceptional 2nd order PDEs via conformal geometry and BGG resolution ⋮ Ordinary differential equations described by their Lie symmetry algebra ⋮ Remarks on non-maximal integral elements of the Cartan plane in jet spaces

Cites Work

• Contact relative differential invariants for non generic parabolic Monge-Ampère equations
• On the integrability of symplectic Monge-Ampère equations
• Normal forms for Lagrangian distributions on 5-dimensional contact manifolds
• On decomposable Monge-Ampère equations
• Classification of Monge–Ampeère Equations
• Integrable Equations of the Dispersionless Hirota type and Hypersurfaces in the Lagrangian Grassmannian
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