Non-isometric Riemannian G-Manifolds with Equal Equivariant Spectra

Abstract

In this paper, the author examines the two methods that people used to systematically construct isospectral non-isometric Riemannian manifolds, the Sunada–Pesce–Sutton method and the torus action method, and shows that both methods can be used to produce equivariantly isospectral non-isometric Riemannian G-manifolds. The author also shows that the Milnor’s isospectral pair is not equivariantly isospectral.

Keywords

Laplacian / Equivariant spectrum / Equivariantly isospectral

Funding

National Nature Science Foundation of China(11571331)