%0 Journal Article %T On the integrability in Grassmann geometries: integrable systems associated with fourfolds Gr(3, 5) %A Boris Doubrov %A Eugene Ferapontov %A Boris Kruglikov %A Vladimir Novikov %J Physics %D 2015 %I arXiv %X We investigate a class of dispersionless integrable systems in 3D associated with fourfolds in the Grassmannian Gr(3, 5), revealing a remarkable correspondence with Einstein-Weyl geometry and the theory of GL(2,R) structures. Generalisations to higher dimensions are also discussed. %U http://arxiv.org/abs/1503.02274v1