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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 and are hermitian.
@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},
pages = {203--243},
publisher = {Scuola normale superiore},
volume = {Ser. 5, 1},
number = {1},
year = {2002},
mrnumber = {1994808},
zbl = {1072.53006},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ASNSP_2002_5_1_1_203_0/}
}
TY - JOUR AU - Apostolov, Vestislav AU - Gauduchon, Paul TI - Selfdual Einstein hermitian four-manifolds JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2002 SP - 203 EP - 243 VL - 1 IS - 1 PB - Scuola normale superiore UR - http://geodesic.mathdoc.fr/item/ASNSP_2002_5_1_1_203_0/ LA - en ID - ASNSP_2002_5_1_1_203_0 ER -
%0 Journal Article %A Apostolov, Vestislav %A Gauduchon, Paul %T Selfdual Einstein hermitian four-manifolds %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2002 %P 203-243 %V 1 %N 1 %I Scuola normale superiore %U http://geodesic.mathdoc.fr/item/ASNSP_2002_5_1_1_203_0/ %G en %F 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://geodesic.mathdoc.fr/item/ASNSP_2002_5_1_1_203_0/