Sunada’s method and the covering spectrum. (English) Zbl 1219.53040

de Smit, Bart; Gornet, Ruth; Sutton, Craig J.

J. Differ. Geom. 86, No. 3, 501-538 (2010).

Every Riemannian manifold has a covering spectrum, defined by Sormani and Wei, related to the length spectrum. This paper gives examples of isospectral compact Riemannian manifolds with distinct covering spectra: the covering spectrum is not a spectral invariant. As indicated in the title, the construction makes use of a well known method of Sunada relating spectra of quotients of compact Riemannian manifolds by finite groups.

Reviewer: Benjamin McKay (Cork)

MSC:

53C20	Global Riemannian geometry, including pinching
53C22	Geodesics in global differential geometry
58J50	Spectral problems; spectral geometry; scattering theory on manifolds

Keywords:

spectral geometry; length spectrum; covering spectrum

Software:

Magma