Geometry and representation of the singular symplectic forms

• Autorzy: Wojciech Domitrz , Stanisław Janeczko , Zbigniew Pasternak-Winiarski
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 57R45: Singularities of differentiable mappings
• 58A10: Differential forms

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2003
• Tom: 62
• Numer: 1
• Strony: 57-71

Daty

wydano

2003

Twórcy

autor

Wojciech Domitrz

• Faculty of Mathematics and Information Science, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warsaw, Poland

autor

Stanisław Janeczko

• Faculty of Mathematics and Information Science, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warsaw, Poland

autor

Zbigniew Pasternak-Winiarski

• Faculty of Mathematics and Information Science, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warsaw, Poland

Identyfikatory

DOI

10.4064/bc62-0-4