Ricci curvature and eigenvalue estimates for the magnetic Laplacian on   manifolds
  In this paper, we present a Lichnerowicz type estimate and (higher order) Buser type estimates for the magnetic Laplacian on a closed Riemannian manifold with a magnetic potential. These results relate eigenvalues, magnetic fields, Ricci curvature, and Cheeger type constants. 
Michela Egidi, Shiping Liu, Florentin M\"unch, and Norbert Peyerimhoff
math.DG