Article #73877

Abstract

We consider the Dirac operator on fibrations over S-1 which have up to holonomy a warped product metric. We give lower bounds for the eigenvalues on M and if the Dirac operator on the typical fibre F has a kernel, we calculate the corresponding part of the spectrum on M explicitly. Moreover, we discuss the dependence of the spectrum of the holonomy and obtain bounds for the multiplicity of the eigenvalues.