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arXiv:math/0004009 [math.DG]AbstractReferencesReviewsResources

On products of harmonic forms

D. Kotschick

Published 2000-04-02, updated 2000-05-21Version 2

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.

Comments: Revised to include flatness of formal metrics on tori of arbitrary dimension
Journal: Duke Math. Journal 107 (2001), 521--531.
Categories: math.DG, math.AG, math.GT, math.SG
Subjects: 53C25, 57R57, 58A14, 57R17
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