%0 Journal Article
%T Positive isotropic curvature and self-duality in dimension 4
%A Thomas Richard
%A Harish Seshadri
%J Mathematics
%D 2013
%I arXiv
%X 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.
%U http://arxiv.org/abs/1311.5256v2