The spectrum on p-forms of a lens space

We give an explicit description of the spectrum of the Hodge–Laplace operator on p -forms of an arbitrary lens space for any p . We write the two generating functions encoding the p -spectrum as rational functions. As a consequence, we prove a geometric characterization of lens spaces that are p -is...

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Bibliographic Details
Published inGeometriae dedicata Vol. 197; no. 1; pp. 107 - 122
Main Author Lauret, Emilio A.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.12.2018
Springer Nature B.V
Subjects
Algebraic Geometry
Convex and Discrete Geometry
Differential Geometry
Hyperbolic Geometry
Lenses
Mathematics
Mathematics and Statistics
Operators (mathematics)
Original Paper
Projective Geometry
Rational functions
Topology
58J53
Isospectrality
One-norm
Lens space
58J50
Spectrum
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Summary:We give an explicit description of the spectrum of the Hodge–Laplace operator on p -forms of an arbitrary lens space for any p . We write the two generating functions encoding the p -spectrum as rational functions. As a consequence, we prove a geometric characterization of lens spaces that are p -isospectral for every p in an interval of the form [ 0 , p 0 ] .
ISSN:0046-5755
1572-9168
DOI:10.1007/s10711-018-0322-9