4-dimensional anti-Kähler manifold; zero scalar curvature; Weyl curvature; flat
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.
 Arthur L. Besse: Einstein manifolds
. Springer Verlag, 1987. MR 0867684
 Andrzej Borowiec, Mauro Francaviglia and Igor Volvovich: Anti-Kählerian Manifolds
. Differential Geometry and its Applications 12 (2000), 281–289. MR 1764334