4-dimensional anti-Kähler manifolds and Weyl curvature
Czechoslovak Mathematical Journal, Tome 56 (2006) no. 1, pp. 267-271.

Voir la notice de l'article dans Czech Digital Mathematics Library

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.
Classification : 32J27, 53B30, 53C25, 53C55, 53C56, 53C80
Mots-clés : 4-dimensional anti-Kähler manifold; zero scalar curvature; Weyl curvature; flat 
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Kim, Jaeman. 4-dimensional anti-Kähler manifolds and Weyl curvature. Czechoslovak Mathematical Journal, Tome 56 (2006) no. 1, pp. 267-271. https://geodesic-test.mathdoc.fr/item/CMJ_2006__56_1_a15/