Orbifold Lens Spaces that are Isospectral but not Isometric

2009/02/14 by Naveed Shamsul Bari, Bari, Naveed Shamsul
Mathematics · #53C20 #Differential Geometry (math.DG) #FOS: Mathematics #Spectral Theory (math.SP) #math.DG #math.SP #msc:53C20

paper · pdf · doi:10.48550/arxiv.0902.2441

66 pages

arxiv created 2009/08/28 · arxiv updated 2009/12/01

Abstract

We answer Mark Kacs famous question - 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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