Orbifold lens spaces that are isospectral but not isometric
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...
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Veröffentlicht in: | Osaka journal of mathematics 2011-03, Vol.48 (no. 1), p.1-40 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | 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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