Einstein metrics, symplectic minimality, and pseudo-holomorphic curves (Q2573742)

Let \((M^ 4,g,\omega)\) be a compact, almost-Kähler-Einstein manifold of negative star-scalar curvature. Then \((M,\omega)\) is a minimal symplectic \(4\)-manifold of general type. In particular, \(M\) cannot be differentiably decomposed as a connected sum \(N \#\; \overline{\mathbb C\mathbb P}_2\).