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