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The 2-Transitive Transplantable Isospectral Drums

The 2-Transitive Transplantable Isospectral Drums

For Riemannian manifolds there are several examples which are isospectral but not isometric, see e.g. J. Milnor [Proc. Nat. Acad. Sci. USA 51 (1964), 542]; in the present paper, we investigate pairs of domains in R² which are isospectral but not congruent. All known such counter examples to M. Kac&#...

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Main Authors: Schillewaert, J., Thas, K.
Format: Article
Language:English
Published: Інститут математики НАН України 2011
Series:Symmetry, Integrability and Geometry: Methods and Applications
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/147407
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spelling irk-123456789-1474072019-02-15T01:23:38Z The 2-Transitive Transplantable Isospectral Drums Schillewaert, J. Thas, K. For Riemannian manifolds there are several examples which are isospectral but not isometric, see e.g. J. Milnor [Proc. Nat. Acad. Sci. USA 51 (1964), 542]; in the present paper, we investigate pairs of domains in R² which are isospectral but not congruent. All known such counter examples to M. Kac's famous question can be constructed by a certain tiling method (''transplantability'') using special linear operator groups which act 2-transitively on certain associated modules. In this paper we prove that if any operator group acts 2-transitively on the associated module, no new counter examples can occur. In fact, the main result is a corollary of a result on Schreier coset graphs of 2-transitive groups. 2011 Article The 2-Transitive Transplantable Isospectral Drums / J. Schillewaert, K. Thas // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 19 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 20D06; 35J10; 35P05; 37J10; 58J53 DOI: http://dx.doi.org/10.3842/SIGMA.2011.080 http://dspace.nbuv.gov.ua/handle/123456789/147407 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description For Riemannian manifolds there are several examples which are isospectral but not isometric, see e.g. J. Milnor [Proc. Nat. Acad. Sci. USA 51 (1964), 542]; in the present paper, we investigate pairs of domains in R² which are isospectral but not congruent. All known such counter examples to M. Kac's famous question can be constructed by a certain tiling method (''transplantability'') using special linear operator groups which act 2-transitively on certain associated modules. In this paper we prove that if any operator group acts 2-transitively on the associated module, no new counter examples can occur. In fact, the main result is a corollary of a result on Schreier coset graphs of 2-transitive groups.
format Article
author Schillewaert, J.
Thas, K.
spellingShingle Schillewaert, J.
Thas, K.
The 2-Transitive Transplantable Isospectral Drums
Symmetry, Integrability and Geometry: Methods and Applications
author_facet Schillewaert, J.
Thas, K.
author_sort Schillewaert, J.
title The 2-Transitive Transplantable Isospectral Drums
title_short The 2-Transitive Transplantable Isospectral Drums
title_full The 2-Transitive Transplantable Isospectral Drums
title_fullStr The 2-Transitive Transplantable Isospectral Drums
title_full_unstemmed The 2-Transitive Transplantable Isospectral Drums
title_sort 2-transitive transplantable isospectral drums
publisher Інститут математики НАН України
publishDate 2011
url http://dspace.nbuv.gov.ua/handle/123456789/147407
citation_txt The 2-Transitive Transplantable Isospectral Drums / J. Schillewaert, K. Thas // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 19 назв. — англ.
series Symmetry, Integrability and Geometry: Methods and Applications
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first_indexed 2023-05-20T17:27:38Z
last_indexed 2023-05-20T17:27:38Z
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