%0 Journal Article %A Doubrov, B. %A Ferapontov, Evgeny %A Kruglikov, B. %A Novikov, Vladimir %D 2017 %T On a class of integrable systems of Monge-Ampere type %U https://repository.lboro.ac.uk/articles/journal_contribution/On_a_class_of_integrable_systems_of_Monge-Ampere_type/9385712 %2 https://repository.lboro.ac.uk/ndownloader/files/16998908 %K System of Monge-Ampere type %K Heavenly-type equation %K Skew-symmetric matrix pencil %K Jordan-Kronecker normal form %K Dispersionless Lax representation %K Linear section of the Grassmannian %K Mathematical Sciences not elsewhere classified %X We investigate a class of multi-dimensional two-component systems of Monge-Ampere 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-Ampere type turn out to be integrable, and can be represented as the commutativity conditions of parameter-dependent vector fields. Geometrically, systems of Monge-Ampere type are associated with linear sections of the Grassmannians. This leads to an invariant differential-geometric characterisation of the Monge-Ampere property. %I Loughborough University