Isospectral metrics on five-dimensional spheres

2001/02/28 by Dorothee Schueth
Mathematics · #math.DG #math.SP #msc:58J53

paper · pdf

published as J. Diff. Geometry 58 (2001), 87 - 111 · 20 pages, AMS-TeX; to appear in: J. Diff. Geometry

arxiv created 2001/09/10 · arxiv updated 2009/11/30

Abstract

We construct isospectral pairs of Riemannian metrics on S⁵ and on B⁶, thus lowering by three the dimension of spheres and balls on which such metrics have been constructed previously (S^{n≥ 8} and B^{n≥ 9}). We also construct continuous families of isospectral Riemannian metrics on S⁷ and on B⁸. 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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