On a class of integrable systems of Monge-Ampère type
Journal article, Peer reviewed
Accepted version
Permanent lenke
http://hdl.handle.net/11250/2483178Utgivelsesdato
2017-06Metadata
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Originalversjon
Dubrov, B. et al. (2017) On a class of integrable systems of Monge-Ampère type. Journal of Mathematical Physics. 58 (6) 10.1063/1.4984982Sammendrag
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 a self-dual Ricci-flat geometry. Based on the Jordan-Kronecker theory of the 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.