Positive isotropic curvature and self-duality in dimension 4

Abstract

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.

14 Pages

References in corpus (2)

• Surgery stable curvature conditions
• Noncoercive Ricci flow invariant curvature cones

Cited by in corpus (2)

• A gauge theoretic approach to Einstein 4-manifolds
• Berger curvature decomposition, Weitzenböck formula, and canonical metrics on four-manifolds