Complete Kähler manifolds with zero Ricci curvature. II.
Shing Tung Yau, Gang Tian (1991)
Inventiones mathematicae
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Complete Kähler manifolds with zero Ricci curvature. II.
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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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