Strongly Isospectral Hyperbolic and Elliptic Manifolds

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.