Geometric formality and non-negative scalar curvature

Abstract

We classify manifolds of small dimension that admit both, a Riemannian metric of non-negative scalar curvature, and a -- 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.

11 pages; improved results in v2; cosmetic changes in v3, v4

Cited by in corpus (1)

• Conformally formal manifolds and the uniformly quasiregular non-ellipticity of $({\mathbb{S}}^2\times {\mathbb{S}}^2)\#({\mathbb{S}}^2\times {\mathbb{S}}^2)$