Geometry of Lagrangian Grassmannians and nonlinear PDEs
Volume 117 / 2019
Banach Center Publications 117 (2019), 9-44
MSC: 35A30, 53C30, 53D10.
DOI: 10.4064/bc117-1
Abstract
This paper contains a thorough introduction to the basic geometric properties of the manifold of Lagrangian subspaces of a linear symplectic space, known as the Lagrangian Grassmannian. It also reviews the important relationship between hypersurfaces in the Lagrangian Grassmannian and second-order PDEs. Equipped with a comprehensive bibliography, this paper has been especially designed as an opening contribution for the proceedings volume of the homonymous workshop held in Warsaw, September 5–9, 2016, and organised by the authors.
