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Geometry and representation of the singular symplectic forms

Tom 62 / 2003

Wojciech Domitrz, Stanis/law Janeczko, Zbigniew Pasternak-Winiarski Banach Center Publications 62 (2003), 57-71 MSC: Primary 57R45; Secondary 58A10 DOI: 10.4064/bc62-0-4

Streszczenie

In this paper we show to what extent the closed, singular $2$-forms are represented, up to the smooth equivalence, by their restrictions to the corresponding singularity set. In the normalization procedure of the singularity set we find the sufficient conditions for the given closed $2$-form to be a pullback of the classical Darboux form. We also find the classification list of simple singularities of the maximal isotropic submanifold-germs in the codimension one Martinet's singular symplectic structures. An example of the exotic singular symplectic structure-germ with no existence of Lagrangian germs is constructed and the singularity theory framework for the pulled back singular symplectic forms is provided.

Autorzy

  • Wojciech DomitrzFaculty of Mathematics and Information Science
    Warsaw University of Technology
    Pl. Politechniki 1
    00-661 Warsaw, Poland
    e-mail
  • Stanis/law JaneczkoFaculty of Mathematics and Information Science
    Warsaw University of Technology
    Pl. Politechniki 1
    00-661 Warsaw, Poland
    e-mail
  • Zbigniew Pasternak-WiniarskiFaculty of Mathematics and Information Science
    Warsaw University of Technology
    Pl. Politechniki 1
    00-661 Warsaw, Poland
    e-mail

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