Displaying similar documents to “On isospectral deformations of riemannian metrics. II”

Hierarchy of integrable geodesic flows.

Peter Topalov (2000)

Publicacions Matemàtiques

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A family of integrable geodesic flows is obtained. Any such a family corresponds to a pair of geodesically equivalent metrics.

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.

Infinitesimal conjugacies and Weil-Petersson metric

Albert Fathi, L. Flaminio (1993)

Annales de l'institut Fourier

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We study deformations of compact Riemannian manifolds of negative curvature. We give an equation for the infinitesimal conjugacy between geodesic flows. This in turn allows us to compute derivatives of intersection of metrics. As a consequence we obtain a proof of a theorem of Wolpert.