NDLI: Flat manifolds isospectral on p-forms

Content Provider	Springer Nature Link
Author	Miatello, R. J. Rossetti, J. P.
Copyright Year	2001
Abstract	We study isospectrality on p-forms of compact flat manifolds by using the equivariant spectrum of the Hodge-Laplacian on the torus. We give an explicit formula for the multiplicity of eigenvalues and a criterion for isospectrality. We construct a variety of new isospectral pairs, some of which are the first such examples in the context of compact Riemannian manifolds. For instance, we give pairs of flat manifolds of dimension n=2p, p≥2, not homeomorphic to each other, which are isospectral on p-forms but not on q-forms for q∈p, 0≤q≤n. Also, we give manifolds isospectral on p-forms if and only if p is odd, one of them orientable and the other not, and a pair of 0-isospectral flat manifolds, one of them Kähler, and the other not admitting any Kähler structure. We also construct pairs, M, M′ of dimension n≥6, which are isospectral on functions and such that β$_{p}$(M)<β$_{p}$(M’), for 0
Starting Page	649
Ending Page	667
Page Count	19
File Format	PDF
ISSN	10506926
Journal	Journal of Geometric Analysis
Volume Number	11
Issue Number	4
e-ISSN	1559002X
Language	English
Publisher	Springer-Verlag
Publisher Date	2001-01-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	isospectral Bieberbach group p-spectrum Differential Geometry Convex and Discrete Geometry Fourier Analysis Abstract Harmonic Analysis Dynamical Systems and Ergodic Theory Global Analysis and Analysis on Manifolds
Content Type	Text
Resource Type	Article
Subject	Geometry and Topology

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