Title: Closed almost-Kähler 4-manifolds of constant non-negative Hermitian holomorphic sectional curvature are Kähler,
Abstract: We show that a closed almost Kähler 4-manifold of globally constant
holomorphic sectional curvature $k\geq 0$ with respect to the canonical
Hermitian connection is automatically Kähler. The same result holds for $k<0$
if we require in addition that the Ricci curvature is J-invariant. The proofs
are based on the observation that such manifolds are self-dual, so that
Chern-Weil theory implies useful integral formulas, which are then combined
with results from Seiberg--Witten theory.