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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Hermitian $ *$-Einstein surfaces


Authors: Geo Grantcharov and Oleg Muškarov
Journal: Proc. Amer. Math. Soc. 120 (1994), 233-239
MSC: Primary 53C25; Secondary 53C55
MathSciNet review: 1186132
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Abstract: We study the problem when a compact Hermitian $ {\ast}$-Einstein surface $ M$ is Kählerian and show that it is true if $ M$ is additionally assumed to be either Einstein or anti-self-dual. We also prove that if the $ {\ast}$-scalar curvature of $ M$ is positive then $ M$ is a conformally Kähler surface with positive first Chern class.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1186132-9
PII: S 0002-9939(1994)1186132-9
Article copyright: © Copyright 1994 American Mathematical Society