Survey of isospectral homogeneous Riemannian manifolds

Abstract

We will review several results on inverse spectral geometry in the setting of homogeneous Riemannian manifolds.Somekey points will beSchueth’s examples ofcontinuous curves of isospectral left-invariant metrics on compact Lie groups, Sutton’s construction of isospectral compact homogeneous Riemannian manifolds(as a generalization of Sunada-Pesce’s method), and spectral isolation/uniqueness problems amongG−invariant metrics on a fixed homogeneous space G/K.