Geometry of Lagrangian Grassmannians and nonlinear PDEs

Tom 117 / 2019

Jan Gutt, Gianni Manno, Giovanni Moreno Banach Center Publications 117 (2019), 9-44 MSC: 35A30, 53C30, 53D10. DOI: 10.4064/bc117-1


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.


  • Jan GuttCenter for Theoretical Physics of the Polish Academy of Sciences
    Al. Lotników 32/46
    02-668 Warsaw, Poland
  • Gianni MannoDipartimento di Scienze Matematiche “G. L. Lagrange”
    Politecnico di Torino
    Corso Duca degli Abruzzi, 24
    10129 Torino, Italy
  • Giovanni MorenoDepartment of Mathematical Methods in Physics
    University of Warsaw
    ul. Pasteura 5
    02-093 Warszawa, Poland

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