Spectra of orbifolds with cyclic fundamental groups

TL;DR

This paper characterizes when orbifolds with cyclic fundamental groups, covered by spheres and projective spaces, are isospectral by analyzing their Laplace-Beltrami spectra twisted by characters, providing explicit spectral descriptions and examples.

Contribution

It offers a simple geometric characterization of isospectral orbifolds with cyclic fundamental groups, including explicit spectral formulas and numerous examples.

Findings

Explicit spectra for orbifolds with cyclic fundamental groups

Characterization of isospectral orbifolds covered by spheres and projective spaces

Many new isospectral examples provided

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 by using generating functions. We also include many isospectral examples.