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Annals of Global Analysis and Geometry

, Volume 34, Issue 4, pp 351–366 | Cite as

Isospectral orbifolds with different maximal isotropy orders

  • Juan Pablo Rossetti
  • Dorothee SchuethEmail author
  • Martin Weilandt
Original Paper

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 operator Isospectral orbifolds Isotropy orders 

Mathematics Subject Classification (2000)

58J53 58J50 53C20 

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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

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

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