  We study a positivity condition for the curvature of oriented Riemannian
4-manifolds: The half-$PIC$ condition. It is a slight weakening of the positive
isotropic curvature ($PIC$) condition introduced by M. Micallef and J. Moore.
  We observe that the half-$PIC$ condition is preserved by the Ricci flow and
satisfies a maximality property among all Ricci flow invariant positivity
conditions on the curvature of oriented 4-manifolds.
  We also study some geometric and topological aspects of half-$PIC$ manifolds.
