Selfdual Einstein hermitian four-manifolds

Apostolov, Vestislav; Gauduchon, Paul

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 1 (2002) no. 1, pp. 203-243.

We provide a local classification of selfdual Einstein riemannian four-manifolds admitting a positively oriented hermitian structure and characterize those which carry a hyperhermitian, non-hyperkähler structure compatible with the negative orientation. We show that selfdual Einstein 4-manifolds obtained as quaternionic quotients of $ℍP^2$ and $ℍH^2$ are hermitian.

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