On products of harmonic forms

By D. Kotschick. 2000

88 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/701c2e1057076a1497659da6c65e1baa7472c6d6

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In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Calabi-Yau connections with torsion on toric bundles (2003, background): “It is known that on most rational surfaces a product of harmonic forms is not harmonic and every harmonic anti-self-dual 2-form has at least one zero [35].”
On formality of generalized symmetric spaces (2001, background): “s notion in the context of generalised symmetric spaces. Although these turn out to be formal in the sense of Sullivan and also satisfy all the restrictions on geometrically formal manifolds found in [9], we shall Date: February 20, 2018; MSC2000: primary 57T15, secondary 53C35, 55P62, 58A14. The au”
Vaisman metrics on solvmanifolds and Oeljeklaus–Toma manifolds (2012, background): “We call a Riemaniann metric formal if all products of harmonic forms are again harmonic (see [20]).”