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On products of harmonic forms

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arxiv math/0004009 v2 pith:FX7UCZQ7 submitted 2000-04-02 math.DG math.AGmath.GTmath.SG

D. Kotschick This is my paper · ORCID
classification math.DGmath.AGmath.GTmath.SG
keywords harmonicformsmanifoldsmetricproductsproveadmitsadmitting
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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.

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  1. Dimensional Reduction and K\"ahler Metric for Metric Moduli in Imaginary Self-Dual Flux

    hep-th 2025-01 conditional novelty 7.0 of 10

    A 10D supergravity reduction derives the 4D moduli space metric for Kähler moduli and, for the first time, for complex structure flat directions in warped type IIB flux compactifications.

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