Reduction techniques for infinite dimensional Hamiltonian systems: some ideas and applications

In the language of tensor analysis on differentaible manifolds we present a reduction method of integrability structures, and apply it to recover some well-known hierarchies of integrable nonlinear evolution equations. The main object dealt with in the paper is the Poisson-Nijenhuis manifold, both in global and in local form: both formulations turn out to be useful, either for theoretical developments or for the applications.