Symplectic realizations of bihamiltonian structures
Abstract
Description
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.
41p. The revised version presents the main result in a more general form. The paper is essentially reconstructed
41p. The revised version presents the main result in a more general form. The paper is essentially reconstructed