The classification of 4-dimensional Kähler manifolds with small eigenvalue of the Dirac operator.
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Huai-Dong Cao, Bennett Chow (1986)
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The aim of this paper is to describe all Kähler manifolds with quasi-constant holomorphic sectional curvature with κ = 0.
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On a 4-dimensional anti-Kähler manifold, its zero scalar curvature implies that its Weyl curvature vanishes and vice versa. In particular any 4-dimensional anti-Kähler manifold with zero scalar curvature is flat.
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