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1 results

  • Une réciproque générique du théorème Sunada

  • HUBERT PESCE
  • Journal:
    Compositio Mathematica / Volume 109 / Issue 3 / December 1997
    Published online by Cambridge University Press:
    04 December 2007, pp. 357-365
    Print publication:
    December 1997
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  • Let $G$ a compact group of isometries of a closed riemannian manifold $(X,m)$. Sunada proved that if $\Gamma_1$ and $\Gamma_2$ are two finite almost-conjugated subgroups of $G$, then $\Gamma_1\setminus X,m)$ and $\Gamma_2\setminus X,m)$ are isospectral. We prove that if $G$ is finite, there exists an open dense set in the set of $G$-invariant metrics for which the converse of this resukt is true. If $G$ is infinite, the situations is more complicated and we obtain some partial results.