Isospectral deformations on Riemannian manifolds which are diffeomorphic to compact Heisenberg manifolds |
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Authors: | Dorothee Schueth |
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Institution: | (1) Math. Inst. Univ. Bonn, Beringstr. 1, D-53115 Bonn, Germany |
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Abstract: | It is known that ifH
m is the classical (2m+1)-dimensional Heisenberg group, Γ a cocompact discrete subgroup ofH
m andg a left invariant metric, then (Γ/H
m, g) is infinitesimally spectrally rigid within the family of left invariant metrics. The purpose of this paper is to show that
for everym≥2 and for a certain choice of Γ andg, there is a deformation (Γ/H
m, g
α) withg=g
1 such that for every α≠1, (Γ/H
m, g
α)does admit a nontrivial isospectral deformation. For α≠1 the metricsg
α will not beH
m-left invariant, and the (Γ/H
m, gxα) will not be nilmanifolds, but still solvmanifolds. |
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Keywords: | |
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