Symplectic realizations of bihamiltonian structures

Details Symplectic realizations of bihamiltonian structures Symplectic realizations of bihamiltonian structures

2000-01-24

arxiv.org/abs/math/0001126v2

Mathematics

Differential Geometry

41p. The revised version presents the main result in a more general form. The paper is essentially reconstructed

Scientific paper

A method of constructing a class of bihamiltonian structures is presented. Elements of this class are generalizations of the so-called bihamiltonian structures of general position on odd-dimensional manifolds. The method consists in a simultaneous reduction of both the real and imaginary parts of a complex symplectic form. Necessary and sufficient conditions of getting a bihamiltonian structure from the mentioned class are obtained. The second part of the paper is devoted to a series of examples of such a reduction related to semisimple Lie algebras.

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