Displaying similar documents to “Continuous families of isospectral metrics on simply connected manifolds.”

Isospectral deformations of closed riemannian manifolds with different scalar curvature

Carolyn S. Gordon, Ruth Gornet, Dorothee Schueth, David L. Webb, Edward N. Wilson (1998)

Annales de l'institut Fourier

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We construct the first examples of continuous families of isospectral Riemannian metrics that are not locally isometric on closed manifolds , more precisely, on S n × T m , where T m is a torus of dimension m ≥ 2 and S n is a sphere of dimension n ≥ 4 . These metrics are not locally homogeneous; in particular, the scalar curvature of each metric is nonconstant. For some of the deformations, the maximum scalar curvature changes during the deformation.

Boundary volume and length spectra of Riemannian manifolds: what the middle degree Hodge spectrum doesn't reveal

Carolyn S. Gordon, Juan Pablo Rossetti (2003)

Annales de l'Institut Fourier

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Let M be a 2 m -dimensional compact Riemannian manifold. We show that the spectrum of the Hodge Laplacian acting on m -forms does not determine whether the manifold has boundary, nor does it determine the lengths of the closed geodesics. Among the many examples are a projective space and a hemisphere that have the same Hodge spectrum on 1- forms, and hyperbolic surfaces, mutually isospectral on 1-forms, with different injectivity radii. The Hodge m -spectrum also does not distinguish orbifolds...

Curvature and the equivalence problem in sub-Riemannian geometry

Erlend Grong (2022)

Archivum Mathematicum

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These notes give an introduction to the equivalence problem of sub-Riemannian manifolds. We first introduce preliminaries in terms of connections, frame bundles and sub-Riemannian geometry. Then we arrive to the main aim of these notes, which is to give the description of the canonical grading and connection existing on sub-Riemann manifolds with constant symbol. These structures are exactly what is needed in order to determine if two manifolds are isometric. We give three concrete examples,...