Lower bounds for eigenvalues of the Dirac operator on n-spheres with SO(n)-symmetry

In this paper we derive estimates for the eigenvalues of the Dirac operator and their multiplicity on manifolds diffeomorphic to Sⁿ with an isometric SO(n)-action. Especially we prove a new lower bound for the first eigenvalue and show an example, where this new bound coincides in the limit with the known upper bounds.