Isospectral Submersion Metrics

Abstract

We construct continuous families of pairwise isospectral metrics on various Riemannian manifolds (e.g., Lie groups, projective spaces and products of these with tori) which arise as quotients of other manifolds. This is done by developing a general principle which guarantees that the torus method can be used to simultaneously construct isospectral metrics on a manifold and a quotient of it. Furthermore, a suffient condition will be given such that the constructed metrics are submersion metrics.