The Warped Product of Hamiltonian Spaces

In this work, the warped product of Hamilton spaces is introduced and it is shown that these spaces obtain Hamiltonian structure as well. Then, the geometric properties of warped product Hamilton spaces such as their nonlinear connections and natural cotangent bundle structures are studied. Moreover, we prove some theorems that show geometric relation between warped product Hamiltonian space and its base Hamiltonian manifolds. For example, we prove that for non-constant warped function $f$, the sasaki lifted metric $G$ of Hamiltonian warped product space is bundle-like for its vertical foliation if and only if based Hamiltonian spaces are Riemannian manifolds.