= Isospectral manifolds
{title2=$\operatorname{Spec}(M)=\operatorname{Spec}(N)$}
= Isospectrality
{synonym}
Two <Riemannian manifolds> are isospectral for a specified <differential operator> if their <eigenvalues>, counted with multiplicities and with the same <boundary conditions>, agree. <Riemannian isometries> preserve the <Laplace-Beltrami operator> <spectrum>, but the converse can fail. The <transplantation theorem> and the <Sunada theorem> give systematic constructions.
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