Isospectral deformations of closed Riemannian manifolds with different scalar curvature

Details Isospectral deformations of closed Riemannian manifolds with different scalar curvature Isospectral deformations of closed Riemannian manifolds with different scalar curvature

1997-10-06

arxiv.org/abs/dg-ga/9710004v1

Ann. Inst. Fourier 48 (1998), no. 2, 593-607

Mathematics

Differential Geometry

amstex, 10 pages, no figures

Scientific paper

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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