Inaudibility of k-D’Atri Properties

Abstract

Working on closed Riemannian manifolds the first author and Schueth gave a list of curvature properties which cannot be determined by the eigenvalue spectrum of the Laplace–Beltrami operator. Following Kac, it is said that such properties are inaudible. Here, we add to that list the dimension of the manifold minus three new properties namely k-D’Atri for k = 3 , … , dim M − 1 .