Annals of Global Analysis and Geometry

, Volume 34, Issue 4, pp 351–366

Isospectral orbifolds with different maximal isotropy orders

  • Juan Pablo Rossetti
  • Dorothee Schueth
  • Martin Weilandt
Original Paper

DOI: 10.1007/s10455-008-9110-3

Cite this article as:
Rossetti, J.P., Schueth, D. & Weilandt, M. Ann Glob Anal Geom (2008) 34: 351. doi:10.1007/s10455-008-9110-3
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Abstract

We construct pairs of compact Riemannian orbifolds which are isospectral for the Laplace operator on functions such that the maximal isotropy order of singular points in one of the orbifolds is higher than in the other. In one type of examples, isospectrality arises from a version of the famous Sunada theorem which also implies isospectrality on p-forms; here the orbifolds are quotients of certain compact normal homogeneous spaces. In another type of examples, the orbifolds are quotients of Euclidean \({\mathbb{R}^3}\) and are shown to be isospectral on functions using dimension formulas for the eigenspaces developed in [12]. In the latter type of examples the orbifolds are not isospectral on 1-forms. Along the way we also give several additional examples of isospectral orbifolds which do not have maximal isotropy groups of different size but other interesting properties.

Keywords

Laplace operatorIsospectral orbifoldsIsotropy orders

Mathematics Subject Classification (2000)

58J5358J5053C20

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • Juan Pablo Rossetti
    • 1
  • Dorothee Schueth
    • 2
  • Martin Weilandt
    • 2
  1. 1.Famaf-CIEMUniversidad Nacional de CórdobaCórdobaArgentina
  2. 2.Institut für MathematikHumboldt-Universität zu BerlinBerlinGermany