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}, zbl = {1072.53006}, mrnumber = {1994808}, language = {en}, url = {http://www.numdam.org/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 DA - 2002/// SP - 203 EP - 243 VL - Ser. 5, 1 IS - 1 PB - Scuola normale superiore UR - http://www.numdam.org/item/ASNSP_2002_5_1_1_203_0/ UR - https://zbmath.org/?q=an%3A1072.53006 UR - https://www.ams.org/mathscinet-getitem?mr=1994808 LA - en ID - ASNSP_2002_5_1_1_203_0 ER -
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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