Almost-Kähler Anti-Self-Dual Metrics

Abstract

We show the existence of strictly almost-Kahler anti-self-dual metrics on certain 4-manifolds by deforming a scalar-flat Kahler metric. On the other hand, we prove the non-existence of such metrics on certain other 4-manifolds by means of Seiberg-Witten theory. In the process, we provide a simple new proof of the fact that any almost-Kahler anti-self-dual 4-manifold must have a non-trivial Seiberg-Witten invariant.