Spectra of orbifolds with cyclic fundamental groups

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 funda...

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Bibliographic Details
Published inAnnals of global analysis and geometry Vol. 50; no. 1; pp. 1 - 28
Main Author Lauret, Emilio A.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.07.2016
Springer Nature B.V
Subjects
Algebra
Analysis
Differential Geometry
Eigenvalues
Geometry
Global Analysis and Analysis on Manifolds
Mathematical models
Mathematical Physics
Mathematics
Mathematics and Statistics
Operators
Quaternions
Spectra
Studies
Theorems
One-norm
Primary 58J50
17B10
Secondary 58J53
Lens space
Isospectral
Cyclic fundamental group
Spectrum
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Summary: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.
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ISSN:0232-704X
1572-9060
DOI:10.1007/s10455-016-9498-0