Isospectral metrics on five-dimensional spheres

Details Isospectral metrics on five-dimensional spheres Isospectral metrics on five-dimensional spheres

2001-02-16

arxiv.org/abs/math/0102126v2

J. Diff. Geometry 58 (2001), 87 - 111

Mathematics

Differential Geometry

20 pages, AMS-TeX; to appear in: J. Diff. Geometry

Scientific paper

We construct isospectral pairs of Riemannian metrics on S^5 and on B^6, thus lowering by three the dimension of spheres and balls on which such metrics have been constructed previously (S^{n\ge 8} and B^{n\ge 9}). We also construct continuous families of isospectral Riemannian metrics on S^7 and on B^8. In each of these examples, the metrics can be chosen equal to the standard metric outside certain subsets of arbitrarily small volume.

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