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Lens Spaces, Isospectral on Forms but not on Functions

Published online by Cambridge University Press:  01 February 2010

Ruth Gornet  and
Jeffrey McGowan
Ruth Gornet
Affiliation:
Department of Mathematics, University of Texas at Arlington, USA, [email protected]
Jeffrey McGowan
Affiliation:
Department of Mathematics, Central Connecticut State University, USA, [email protected]

Abstract

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We study the p-form spectrum of the Laplace-Beltrami operator acting on lens spaces as considered by Ikeda [Geometry of manifolds (Academic Press, Boston, MA, 1989) 383–417]. Ikeda gave examples of such spaces that are non-isometric but isospectral for all p ≤ p0. In this paper we exhibit examples of such spaces that are not isometric, and are isospectral for various, but not for all. values of p. In particular, examples are given of non-isometric lens spaces that are isospectral for some values of p but not for the case p = 0.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 9 , 2006 , pp. 270 - 286
Copyright
Copyright © London Mathematical Society 2006

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Supplementary material: File

JCM 9 Gornet and McGowan Appendix B Part 1

Gornet and McGowan Appendix B Part 1

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JCM 9 Gornet and McGowan Appendix B Part 2

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JCM 9 Gornet and McGowan Appendix B Part 3

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JCM 9 Gornet and McGowan Appendix C Part 1

Gornet and McGowan Appendix C Part 1

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JCM 9 Gornet and McGowan Appendix C Part 2

Gornet and McGowan Appendix C Part 2

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JCM 9 Gornet and McGowan Appendix C Part 3

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JCM 9 Gornet and McGowan Appendix D

Gornet and McGowan Appendix D

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