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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

We construct the first examples of continuous families of isospectral Riemannian metrics that are not locally isometric on closed manifolds , more precisely, on $S^{n} \times T^{m}$ , where $T^{m}$ is a torus of dimension $m \geq 2$ and $S^{n}$ is a sphere of dimension $n \geq 4$ . 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.

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