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Article

Kim, Jaeman
4-dimensional anti-Kähler manifolds and Weyl curvature. (English). Czechoslovak Mathematical Journal, vol. 56 (2006), issue 1, pp. 267-271
MSC: 32J27, 53B30, 53C25, 53C55, 53C56, 53C80 | MR 2207017 | Zbl 1157.53316
Keywords:
4-dimensional anti-Kähler manifold; zero scalar curvature; Weyl curvature; flat
Summary:
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.
References:
[1] Arthur L. Besse: Einstein manifolds. Springer Verlag, 1987. MR 0867684
[2] Andrzej Borowiec, Mauro Francaviglia and Igor Volvovich: Anti-Kählerian Manifolds. Differential Geometry and its Applications 12 (2000), 281–289. MR 1764334
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