Normal forms of Poisson structures near a symplectic leaf

2004/03/08 by Olivier Brahic, Brahic, Olivier · 1 citation
Mathematics · #53D17 (primary) 70G45 (secondary) #Advanced Algebra and Geometry #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #math.DG #math.SG #msc:53D17 #msc:70G45

paper · pdf · doi:10.48550/arxiv.math/0403136

8 pages

arxiv created 2004/03/08 · openalex publication_date 2004/03/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show how one can handle the formalism developped by Yurii Vorobjev in order to give general results about the problems of linearisation and of normal form of a Poisson structure in the neighborhood of one of its symplectic leaves.

Cited by

• Nonlinearizability of certain Poisson structures near a symplectic leaf

Related

• Nonlinearizability of certain Poisson structures near a symplectic leaf
• Normal forms in Poisson geometry
• Normal forms for Poisson maps and symplectic groupoids around Poisson\n transversals
• Poisson geometry around Poisson submanifolds
• Poisson Equivalence over a Symplectic Leaf