A classification of Monge-Ampère equations

DOI10.24033/asens.1673zbMath0789.58078OpenAlexW2066553128MaRDI QIDQ4272537

Vladimir Rubtsov, Igor V. Chekalov, Valentin V. Lychagin

Publication date: 6 December 1993

Published in: Annales scientifiques de l'École normale supérieure (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=ASENS_1993_4_26_3_281_0

zbMATH Keywords

differential formscontact geometryjet bundlesMonge-Ampère equations

Mathematics Subject Classification ID

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

Related Items (22)

Soliton solutions of the mean curvature flow and minimal hypersurfaces ⋮ SINGULARITIES OF IMPROPER AFFINE SPHERES AND SURFACES OF CONSTANT GAUSSIAN CURVATURE ⋮ Monge-Ampère equations and generalized complex geometry -- the two-dimensional case ⋮ APPLICATION OF CARTAN’S EQUIVALENCE METHOD TO DISTRIBUTION OF PLANES ⋮ On differential equations characterized by their Lie point symmetries ⋮ On a generalization of Monge-Ampère equations and Monge-Ampère systems ⋮ Clifford structures, bilegendrian surfaces, and extrinsic curvature ⋮ On symplectic classification of effective 3-forms and Monge-Ampère equations. ⋮ Lie solutions of Riemannian transport equations on compact manifolds ⋮ Second-order type-changing evolution equations with first-order intermediate equations ⋮ A geometric interpretation of coherent structures in Navier–Stokes flows ⋮ Compatible structures on Lie algebroids and Monge-Ampère operators ⋮ Transformation of hyperbolic Monge-Ampère equations into linear equations with constant coefficients ⋮ Solutions surfaces of Monge-Ampère equations ⋮ Generalized Kähler-Ricci flow and the classification of nondegenerate generalized Kähler surfaces ⋮ On the integrability of symplectic Monge-Ampère equations ⋮ Complex solutions of Monge-Ampère equations ⋮ Contact linearization of nondegenerate Monge-Ampère equations ⋮ Anti-self-dual gravitational metrics determined by the modified heavenly equation ⋮ Differential invariants of generic hyperbolic Monge-Ampère equations ⋮ An extension of the Siegel space of complex abelian varieties and conjectures on stability structures ⋮ Pseudo-Riemannian and Hessian geometry related to Monge-Ampère structures

Cites Work

• Faisceaux algébriques cohérents
• The infinite groups of Lie and Cartan. I: The transitive groups
• Integrability criteria for systems of nonlinear partial differential equations
• LOCAL CLASSIFICATION OF NON-LINEAR FIRST ORDER PARTIAL DIFFERENTIAL EQUATIONS
• ON SUFFICIENT ORBITS OF A GROUP OF CONTACT DIFFEOMORPHISMS
• Overdetermined systems of linear partial differential equations
• A Classification of Spinors Up to Dimension Twelve
• An algebraic model of transitive differential geometry
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