On products of harmonic forms

Details On products of harmonic forms On products of harmonic forms

2000-04-02

arxiv.org/abs/math/0004009v2

Duke Math. Journal 107 (2001), 521--531.

Mathematics

Differential Geometry

Revised to include flatness of formal metrics on tori of arbitrary dimension

Scientific paper

10.1215/S0012-7094-01-10734-5

We prove that manifolds admitting a Riemannian metric for which products of harmonic forms are harmonic satisfy strong topological restrictions, some of which are akin to properties of flat manifolds. Others are more subtle, and are related to symplectic geometry and Seiberg-Witten theory. We also prove that a manifold admits a metric with harmonic forms whose product is not harmonic if and only if it is not a rational homology sphere.

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