On a Poisson reduction for Gel'fand--Zakharevich manifolds

Abstract

We formulate and discuss a reduction theorem for Poisson pencils associated with a class of integrable systems, defined on bi-Hamiltonian manifolds, recently studied by Gel'fand and Zakharevich. The reduction procedure is suggested by the bi-Hamiltonian approach to the Separation of Variables problem.Comment: Latex, 14 pages. Proceeding of the Conference "Multi-Hamiltonian Structures: Geometric and Algebraic Aspects". August 9-18, 2001 Bedlewo, Poland. To appear in ROM