= Sunada theorem
{c}
= Sunada's theorem
{c}
{synonym}
Suppose a finite <group> $G$ acts by <Riemannian isometries> on a compact <Riemannian manifold> $M$, and <Gassmann equivalent> subgroups $H_1,H_2$ act freely. The quotient manifolds $H_i\backslash M$ have equal <Laplace-Beltrami operator> spectra. For an <eigenfunction> space $E$, the quotient multiplicity is $|H_i|^{-1}\sum_{h\in H_i}\operatorname{tr}(h|E)$, and the equality follows by summing its <character of a representation> over <conjugacy classes>. Nonconjugacy inside $G$ alone does not guarantee that the quotients are nonisometric.
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