Isospectral deformations of closed Riemannian manifolds with different scalar curvature

DOI10.5802/aif.1630zbMath0922.58083arXivdg-ga/9710004OpenAlexW2035410908WikidataQ115159054 ScholiaQ115159054MaRDI QIDQ1266228

Ruth Gornet, Dorothee Schueth, David L. Webb, Edward N. Wilson, Carolyn S. Gordon

Publication date: 14 September 1998

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/dg-ga/9710004

zbMATH Keywords

scalar curvaturespectral geometryisospectral deformations

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Nilpotent and solvable Lie groups (22E25) Global Riemannian geometry, including pinching (53C20)

Related Items (10)

Boundary volume and length spectra of Riemannian manifolds: what the middle degree Hodge spectrum doesn't reveal. ⋮ 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 ⋮ Inaudibility of sixth order curvature invariants ⋮ On inaudible curvature properties of closed Riemannian manifolds ⋮ Non-Sunada graphs ⋮ The length spectrum of Riemannian two-step nilmanifolds1 ⋮ Isospectral metrics and potentials on classical compact simple Lie groups ⋮ Isospectral deformations of negatively curved Riemannian manifolds with boundary which are not locally isometric. ⋮ Lens Spaces, Isospectral on Forms but not on Functions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Isospectral closed Riemannian manifolds which are not locally isometric
• Isospectral deformations of compact solvmanifolds
• Isospectral Riemann surfaces
• Riemannian coverings and isospectral manifolds
• The spectrum of the Laplacian on Riemannian Heisenberg manifolds
• Isospectral and non-isometric Riemannian manifolds
• Isometry groups on homogeneous nilmanifolds
• Isospectral plane domains and surfaces via Riemannian orbifolds
• Locally non-isometric yet super isospectral spaces
• Continuous families of isospectral Riemannian metrics which are not locally isometric
• Continuous families of Riemannian manifolds, isospectral on functions but not on 1-forms
• Isospectral deformations on Riemannian manifolds which are diffeomorphic to compact Heisenberg manifolds
• A new construction of isospectral Riemannian nilmanifolds with examples
• Isospectral deformations II: Trace formulas, metrics, and potentials
• Isospectral surfaces of small genus
• Isospectral deformations I: Riemannian structures on two-step nilspaces
• Constructing Isospectral Manifolds
• On lens spaces which are isospectral but not isometric
• Geometry of 2-Step Nilpotent Groups with a Left Invariant Metric. II
• EIGENVALUES OF THE LAPLACE OPERATOR ON CERTAIN MANIFOLDS

This page was built for publication: Isospectral deformations of closed Riemannian manifolds with different scalar curvature