Abstract
In this paper, we prove that two compact hyperbolic manifolds Γ1\\Hn and Γ2\\Hn are strongly isospectral if and only if the regular representations of the full group G of isometries of the hyperbolic space Hn into L2(Γ1\\G) and L2(Γ2\\G) are equivalent. The same result is proved for elliptic manifolds.
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