Isospectral deformations of negatively curved Riemannian manifolds with boundary which are not locally isometric

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dc.creatorGordon, Carolyn S.
dc.creatorSzabo, Zoltan I.
dc.date2000-03-01
dc.date.accessioned2026-07-07T04:34:09Z
dc.date.available2026-07-07T04:34:09Z
dc.descriptionTo what extent does the eigenvalue spectrum of the Laplace-Beltrami operator on a compact Riemannian manifold determine the geometry of the manifold? We give examples of isospectral manifolds with different local geometry including continuous families of isospectral negatively curved manifolds with boundary as well as various pairs of manifolds. The latter illustrate that the spectrum does not determine whether a manifold with boundary has negative curvature, whether it has constant Ricci curvature, and whether it has parallel curvature tensor, and the spectrum does not determine whether a closed manifold has constant scalar curvature.
dc.description21 pages
dc.identifierhttps://arxiv.org/abs/math/0003007
dc.identifierhttp://arxiv.org/abs/math/0003007
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58795
dc.subjectDifferential Geometry
dc.subjectSpectral Theory
dc.titleIsospectral deformations of negatively curved Riemannian manifolds with boundary which are not locally isometric
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