The Local Product Theorem for bihamiltonian structures

Details The Local Product Theorem for bihamiltonian structures The Local Product Theorem for bihamiltonian structures

2011-07-12

arxiv.org/abs/1107.2243v1

Mathematics

Symplectic Geometry

75 pages, no figures

Scientific paper

In this work one proves that, around each point of a dense open set (regular points), a real analytic or holomorphic bihamiltonian structure decomposes into a product of a Kronecker bihamiltonian structure and a symplectic one if a necessary condition on the characteristic polynomial of the symplectic factor holds. Moreover we give an example of bihamiltonian structure for showing that this result does not extend to the $C^\infty$-category. Thus a classical problem on the geometric theory of bihamiltonian structures is solved at almost every point.

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