Almost-Kähler anti-self-dual metrics (Q300427)

The author of the paper shows existence of a strictly almost-Kähler anti-self-dual metric on certain compact smooth four-dimensional manifolds which admits a scalar-flat Kähler metric, by deformations. The author also shows the existence of a non-trivial solution of Seiberg-Witten equations of almost Kähler anti-self-dual 4-manifolds. In the end, the author classifies almost Kähler ASD-metric compact 4-manifolds also admitting a metric of positive scalar curvature.