Commentarii Mathematici Helvetici
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Published online: 2002-12-31
Isospectral simply-connected homogeneous spaces and the spectral rigidity of group actionsC. J. Sutton (1) University of Pennsylvania, Philadelphia, USA
We generalize Sunada's method to produce new examples of closed, locally non-isometric manifolds which are isospectral. In particular, we produce pairs of isospectral, simply-connected, locally non-isometric normal homogeneous spaces. These pairs also allow us to see that in general group actions with discrete spectra are not determined up to measurable conjugacy by their spectra. In particular, we show this for lattice actions.
Keywords: Spectral geometry, Laplace operator, homogeneous spaces, group actions
Sutton C.: Isospectral simply-connected homogeneous spaces and the spectral rigidity of group actions. Comment. Math. Helv. 77 (2002), 701-717. doi: 10.1007/PL00012438