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Currently displaying 1 – 3 of 3

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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

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 from manifolds....

Isospectral hyperbolic surfaces have matching geodesics.

Doyle, Peter G.; Rossetti, Juan Pablo — 2008

The New York Journal of Mathematics [electronic only]

Tetra and Didi, the cosmic spectral twins.

Doyle, Peter G.; Rossetti, Juan Pablo — 2004

Geometry & Topology

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