Two closed Riemannian manifolds are called isospectral, if the Laplace operators on them have the same set of eigenvalues counted with multiplicities. Riemannian manifolds which are isometric are trivially isospectral and up to date there are only two methods to systematically construct isospectral, but not isometric, manifolds: the Sunada method and the construction via effective torus actions. In this thesis we investigate the question whether isospectral metrics constructed via effective torus actions descend along Riemannian covering maps. This is used to construct continuous families of isospectral, not isometric metrics on certain lens spaces of dimension at least seven, on the spaces RP^(2m-1>= 5) x S1 and on the Lie group SO(3) x S^1.     «

Two closed Riemannian manifolds are called isospectral, if the Laplace operators on them have the same set of eigenvalues counted with multiplicities. Riemannian manifolds which are isometric are trivially isospectral and up to date there are only two methods to systematically construct isospectral, but not isometric, manifolds: the Sunada method and the construction via effective torus actions. In this thesis we investigate the question whether isospectral metrics constructed via effective toru...     »