A new construction of isospectral Riemannian nilmanifolds with examples

DOI10.1307/mmj/1029005395zbMath0851.53024arXivmath/9502208OpenAlexW2093720465WikidataQ115238973 ScholiaQ115238973MaRDI QIDQ1916876

Ruth Gornet

Publication date: 10 November 1996

Published in: Michigan Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9502208

zbMATH Keywords

spectral geometryisospectralitypairs of isospectral nilmanifolds

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Global Riemannian geometry, including pinching (53C20)

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Boundary volume and length spectra of Riemannian manifolds: what the middle degree Hodge spectrum doesn't reveal. ⋮ Dirac operator spectrum on a nilmanifold ⋮ The geometry of filiform nilpotent Lie groups ⋮ Isospectral potentials and conformally equivalent isospectral metrics on spheres, balls and Lie groups ⋮ Length minimizing geodesics and the length spectrum of Riemannian two-step nilmanifolds ⋮ Spectral theory of a class of nilmanifolds attached to Clifford modules ⋮ The minimal marked length spectrum of Riemannian two-step nilmanifolds ⋮ Laplacian spectrum on a nilmanifold, truncations and effective theories ⋮ Riemannian nilmanifolds and the trace formula ⋮ Isospectral deformations of closed Riemannian manifolds with different scalar curvature ⋮ Can One Hear the Shape of a Group? ⋮ The length spectrum of Riemannian two-step nilmanifolds1 ⋮ Isospectral deformations of negatively curved Riemannian manifolds with boundary which are not locally isometric. ⋮ Continuous families of Riemannian manifolds, isospectral on functions but not on 1-forms ⋮ Lens Spaces, Isospectral on Forms but not on Functions

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