Published 02 Nov 2006. First received 09 Jan 2006.

Lens spaces, isospectral on forms but not on functions

Ruth Gornet and Jeffrey McGowan

Abstract: The authors 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 the authors 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.

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In addition to the paper, the following electronic appendices are available to subscribers :

Appendix B : This appendix contains links to MATHEMATICA notebooks with code to generate the examples cited in the paper.

Appendix C : This appendix contains PDF files with the code and computations used to generate the examples cited in the paper.

Appendix D : This appendix contains the original MAPLE code used to generate the examples cited in the paper.

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