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

Accepted in Annals of Global Analysis and Geometry

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Cited by in corpus (6)

• The spectrum on $p$-forms of a lens space
• Multiplicity formulas for fundamental strings of representations of classical Lie algebras
• A computational study on lens spaces isospectral on forms
• Recent results on the spectra of lens spaces
• Weight multiplicity formulas for bivariate representations of classical Lie algebras
• Harmonic-Counting Measures and Spectral Theory of Lens Spaces