Isospectral Metrics on Five-Dimensional Spheres

Abstract

We construct isospectral pairs of Riemannian metrics on S⁵ and on B⁶, thus lowering by three the minimal dimension of spheres and balls on which such metrics have been constructed previously (S^n≥8 and B^n≥9). We also construct continuous families of isospectral Riemannian metrics on S⁷ and on B⁸. In each of these examples, the metrics can be chosen equal to the standard metric outside certain subsets of arbitrarily small volume.