For a (compact) spin manifold, we know that the eigenvalues of the Laplace = Dirac$^2$ operator tend to infinity, since it is an elliptic differential operator. I am wonder for the space, or gap, between the eigenvalues as we tend to infinity - will they become as large as we want, or at least is there a minimum distance between succesive eigenvalues.

(Honestly, I care most about Hermitian manifolds that are spin, so if it is easier in this case, please let me know!)