Lower bounds for eigenvalues of the Dirac operator on surfaces of rotation (Q1806042)

The author studies the eigenvalues of the Dirac operator on a two-dimensional sphere equipped with a Riemannian metric that is invariant under a free circle action. Let \(f_{\max}\) be the maximal length of an orbit. Then she proves the theorem: Any eigenvalue \(\lambda\) of the Dirac operator satisfies \(|\lambda |\geq {1\over 2 f_{\max}}\). The multiplicity of an eigenvalue \(\lambda_n\), \(n>0\) with \({2n-1\over 2f_{\max}}\leq \lambda_n \leq {2n+1\over 2f_{\max}}\) is at most \(2n\).