On a class of integrable systems of Monge-Ampère type

Abstract

We investigate a class of multi-dimensional two-component systems of Monge-Ampère type that can be viewed as generalisations of heavenly-type equations appearing in self-dual Ricci-flat geometry. Based on the Jordan-Kronecker theory of skew-symmetric matrix pencils, a classification of normal forms of such systems is obtained. All two-component systems of Monge-Ampère type turn out to be integrable, and can be represented as the commutativity conditions of parameter-dependent vector fields. Geometrically, systems of Monge-Ampère type are associated with linear sections of the Grassmannians. This leads to an invariant differential-geometric characterisation of the Monge-Ampère property.

arXiv admin note: text overlap with arXiv:1503.02274

References in corpus (2)

• Inverse Scattering Problem for Vector Fields and the Cauchy Problem for the Heavenly Equation
• Monge-Ampere equations and generalized complex geometry. The two-dimensional case

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• Integrability of dispersionless Hirota type equations in 4D and the symplectic Monge-Ampere property