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Representation Equivalent Bieberbach Groups and Strongly Isospectral Flat Manifolds

  • Emilio A. Lauret (a1)

Let Γ1 and Γ2 be Bieberbach groups contained in the full isometry group G of ℝ n . We prove that if the compact flat manifolds Γ1\ℝn and Γ2\ℝn are strongly isospectral, then the Bieberbach groups Γ1 and Γ2 are representation equivalent; that is, the right regular representations L 21\G) and L 22\G) are unitarily equivalent.

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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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