  This paper is concerned with the existence of periodic orbits on energy
hypersurfaces in cotangent bundles of Riemannian manifolds defined by
mechanical Hamiltonians. In \cite{bpv} it was proved that, provided certain
geometric assumptions are satisfied, regular mechanical hypersurfaces in
$\mathbb{R}^{2n}$, in particular non-compact ones, contain periodic orbits if
one homology group among the top half does not vanish. In the present paper we
extend the above mentioned existence result to a class of hypersurfaces in
cotangent bundles of Riemannian manifolds with flat ends.
