Symplectic realizations of bihamiltonian structures
Differential Geometry
2007-05-23 v2
Abstract
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.
Cite
@article{arxiv.math/0001126,
title = {Symplectic realizations of bihamiltonian structures},
author = {Andriy Panasyuk},
journal= {arXiv preprint arXiv:math/0001126},
year = {2007}
}
Comments
41p. The revised version presents the main result in a more general form. The paper is essentially reconstructed