Landau ground state on Riemannian surfaces

In this paper, the authors study the ground state of a particle moving on an even-dimensional Riemannian manifold (M,gμν under the action of a nondegenerate magnetic field Bμ,ν in the hypothesis that the metric and the symplectic two-form provided by B, define a conformal Kahler structure on M. On a Riemannian surface the Hamiltonian always has a degenerate ground state and in the compact case its degeneration is equal to the volume of the surface in h units minus one half of the Euler-Poincare characteristic