Selfdual Einstein hermitian four-manifolds

Apostolov, Vestislav; Gauduchon, Paul

Apostolov, Vestislav ; Gauduchon, Paul

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

Résumé

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

ℍ P^{2}

and

ℍ H^{2}

are hermitian.

MR 1994808 | Zbl 1072.53006

Classification: 53B35, 53C55

@article{ASNSP_2002_5_1_1_203_0,
     author = {Apostolov, Vestislav and Gauduchon, Paul},
     title = {Selfdual Einstein hermitian four-manifolds},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 5, 1},
     number = {1},
     year = {2002},
     pages = {203-243},
     zbl = {1072.53006},
     mrnumber = {1994808},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2002_5_1_1_203_0}
}

Apostolov, Vestislav; Gauduchon, Paul. Selfdual Einstein hermitian four-manifolds. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 1 (2002) no. 1, pp. 203-243. http://www.numdam.org/item/ASNSP_2002_5_1_1_203_0/

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