Integrability Conditions For Almost Hermitian And Almost Kaehler 4-Manifolds

Klaus-Dieter Kirchberg

If $W_{+}$ denotes the self dual part of the Weyl tensor of any Kähler 4-manifold and $S$ its scalar curvature, then the relation $|W_{+}{|}^2=S^2/6$ is well-known. For any almost Kähl…