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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
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Abstract

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 $m\ge 2$ and $S^n$ is a sphere of dimension $n\ge 4$. 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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BibTeXRIS

Carolyn S. Gordon, Ruth Gornet, Dorothee Schueth, David. L. Webb, Edward N. Wilson. 1997-10-06. Isospectral deformations of closed Riemannian manifolds with different scalar curvature. https://arxiv.org/abs/dg-ga/9710004

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