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Journal of the London Mathematical Society 2006 73(1):194-208; doi:10.1112/S0024610705022532
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© The London Mathematical Society

Normal Forms for Two Classes of Exact Poisson Structures in Dimension Four

I. Cruz and H. Mena-Matos

Centro de Matemática da Universidade do Porto, Departamento de Matemática Aplicada Faculdade de Ciências da Universidade do Porto, Campo Alegre, 687,4169-007 Porto, Portugal imcruz{at}fc.up.pt
Centro de Matemática da Universidade do Porto, Departamento de Matemática Aplicada Faculdade de Ciências da Universidade do Porto, Campo Alegre, 687,4169-007 Porto, Portugal mmmatos{at}fc.up.pt

Received 29 July 2003. Revision received 30 March 2004.

We consider singular exact Poisson structures on an oriented manifold of dimension 4. Using normal forms for divergence-free vector fields on R3 and for 1-parameter deformations of functions on R3 we produce normal forms for two classes of such Poisson structures around the singular point.


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