Spectra of orbifolds with cyclic fundamental groups

Abstract

We give a simple geometric characterization of isospectral orbifolds covered by spheres, complex projective spaces and the quaternion projective line having cyclic fundamental group. The differential operators considered are Laplace–Beltrami operators twisted by characters of the corresponding fundamental group. To prove the characterization, we first give an explicit description of their spectra using generating functions. We also include many isospectral examples.