On a Poisson reduction for Gel'fand--Zakharevich manifolds
  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. 
G. Falqui and M. Pedroni