Pure and Applied Mathematics Quarterly
Volume 13 (2017)
Special Issue in Honor of Simon Donaldson
Guest Editors: Kefeng Liu, Richard Thomas, and Shing-Tung Yau
Geometric formality and non-negative scalar curvature
Pages: 437 – 451
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.
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