Duke Mathematical Journal

On products of harmonic forms

D. Kotschick

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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.

Article information

Duke Math. J. Volume 107, Number 3 (2001), 521-531.

First available in Project Euclid: 5 August 2004

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)
Secondary: 53D35: Global theory of symplectic and contact manifolds [See also 57Rxx] 57R17: Symplectic and contact topology 57R57: Applications of global analysis to structures on manifolds, Donaldson and Seiberg-Witten invariants [See also 58-XX] 58A14: Hodge theory [See also 14C30, 14Fxx, 32J25, 32S35]


Kotschick, D. On products of harmonic forms. Duke Math. J. 107 (2001), no. 3, 521--531. doi:10.1215/S0012-7094-01-10734-5. http://projecteuclid.org/euclid.dmj/1091737022.

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