Hamiltonian integrable systems in a magnetic field and symplectic-Haantjes geometry

We investigate the geometry of classical Hamiltonian systems immersed in a magnetic field in three-dimensional (3D) Riemannian configuration spaces. We prove that these systems admit non-trivial symplectic-Haantjes manifolds, which are symplectic manifolds endowed with an algebra of Haantjes (1,1)-tensors. These geometric structures allow us to determine separation variables for known systems algorithmically. In addition, the underlying St & auml;ckel geometry is used to construct new families of integrable Hamiltonian models immersed in a magnetic field.