Geometric formality and non-negative scalar curvature
  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. 
D. Kotschick
math.DG math.GT