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

Abstract

In this paper we derive estimates for the eigenvalues of the Dirac operator and their multiplicity on manifolds diffeomorphic to S-n 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. (C) 2000 Elsevier Science B.V. All right reserved. Subj. Class.: Differential Geometry 1991 MSC: 53C25: 58G25: 58G35.