On a class of integrable systems of Monge-Amp\`ere type
Abstract
We investigate a class of multi-dimensional two-component systems of Monge-Amp\`ere 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-Amp\`ere type turn out to be integrable, and can be represented as the commutativity conditions of parameter-dependent vector fields. Geometrically, systems of Monge-Amp\`ere type are associated with linear sections of the Grassmannians. This leads to an invariant differential-geometric characterisation of the Monge-Amp\`ere property.
Keywords
Cite
@article{arxiv.1701.02270,
title = {On a class of integrable systems of Monge-Amp\`ere type},
author = {Boris Doubrov and Eugene Ferapontov and Boris Kruglikov and Vladimir Novikov},
journal= {arXiv preprint arXiv:1701.02270},
year = {2017}
}
Comments
arXiv admin note: text overlap with arXiv:1503.02274