On products of harmonic forms
D. Kotschick
Source: Duke Math. J. Volume 107, Number 3
(2001), 521-531.
Abstract
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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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1091737022
Mathematical Reviews number (MathSciNet): MR1828300
Digital Object Identifier: doi:10.1215/S0012-7094-01-10734-5
Zentralblatt MATH identifier: 1036.53030
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