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March 2011 Orbifold lens spaces that are isospectral but not isometric
Naveed Shams Ul Bari
Osaka J. Math. 48(1): 1-40 (March 2011).


We answer Mark Kac's famous question [13], ``can one hear the shape of a drum?'' in the negative for orbifolds that are spherical space forms. This is done by extending the techniques developed by A. Ikeda on lens spaces to the orbifold setting. Several results are proved to show that with certain restrictions on the dimensionalities of orbifold lens spaces we can obtain infinitely many pairs of isospectral non-isometric lens spaces. These results are then generalized to show that for any dimension greater than 8 we can have pairs of isospectral non-isometric orbifold lens spaces.


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Naveed Shams Ul Bari. "Orbifold lens spaces that are isospectral but not isometric." Osaka J. Math. 48 (1) 1 - 40, March 2011.


Published: March 2011
First available in Project Euclid: 22 March 2011

zbMATH: 1229.58027
MathSciNet: MR2802590

Primary: 58J53
Secondary: 53C20

Rights: Copyright © 2011 Osaka University and Osaka City University, Departments of Mathematics


Vol.48 • No. 1 • March 2011
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