A new method for eigenvalue estimates for Dirac operators on certain manifolds with Sk-symmetry

Abstract

We prove estimates for the first nonnegative eigenvalue of the Dirac operator on certain manifolds with SO(k + 1)-symmetry in terms of geometric properties of the manifold. For the proof we employ an abstract technique which is new in this context and may apply to other cases of manifolds as well. (C) 2002 Published by Elsevier Science B.V.