Bi-Hamiltonian Structures on the Tangent Bundle to a Poisson Manifold

Abstract

Communicated by Alexandar B. Yanovski Abstract. In the case when M is equipped with a bi-Hamiltonian structure (M,π1, π2) we show how to construct family of Poisson structures on the tangent bundle TM to a Poisson manifold. Moreover we present how to find Casimir functions for those structures and we discuss some particular examples. MSC : 53D17, 37K10