Geometric formality and non-negative scalar curvature

We classify manifolds of small dimensions that admit both a Riemannian metric of non-negative scalar curvature, and an a priori different metric for which all wedge products of harmonic forms are harmonic. For manifolds whose first Betti numbers are sufficiently large, this classification extends to higher dimensions.

2010 Mathematics Subject Classification

Primary 53C25. Secondary 53C43, 57M50, 57R17, 57R57, 58A14.

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Research done at the Institute for Advanced Study in Princeton with the support of The Fund For Math and The Oswald Veblen Fund.

Received 4 July 2017

Published 12 November 2018