Some remarks on the construction of bihamiltonian manifolds

From the MR review by M.Modugno: "The paper deals with different constructions of bi-Hamiltonian manifolds, i.e., manifolds M equipped with two skew-symmetric contravariant 2-tensors P and Q , such that [P,P]=[Q,Q]=[P,Q]=0, where [ , ] is the Schouten bracket. The first construction can arise from the infinitesimal deformation of a Poisson manifold (M,P) with respect to a given vector field of the manifold. A second construction is a reduction based on the search for suitable bi-Hamiltonian submanifolds of a given bi-Hamiltonian manifold (M,P,Q). The two approaches are compared and discussed in the cases when M is the dual of a Lie algebra. An application is obtained by considering the above methods for a Lie algebra of formal series, which is related to the so called polynomial spectral problem."