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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

On conformally Kähler, Einstein manifolds


Authors: Xiuxiong Chen, Claude LeBrun and Brian Weber
Journal: J. Amer. Math. Soc. 21 (2008), 1137-1168
MSC (2000): Primary 53C55; Secondary 14J80, 53A30, 53C25
Published electronically: January 28, 2008
MathSciNet review: 2425183
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Abstract: We prove that any compact complex surface with $ c_1>0$ admits an Einstein metric which is conformally related to a Kähler metric. The key new ingredient is the existence of such a metric on the blow-up $ \mathbb{CP}_2\char93 2\overline{\mathbb{CP}_2}$ of the complex projective plane at two distinct points.


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Additional Information

Xiuxiong Chen
Affiliation: Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Dr, Madison, Wisconsin 53706-1388
Email: xiu@math.wisc.edu

Claude LeBrun
Affiliation: Department of Mathematics, State University of New York, Stony Brook, New York 11794-3651
Email: claude@math.sunysb.edu

Brian Weber
Affiliation: Department of Mathematics, State University of New York, Stony Brook, New York 11794-3651
Email: brweber@math.sunysb.edu

DOI: http://dx.doi.org/10.1090/S0894-0347-08-00594-8
PII: S 0894-0347(08)00594-8
Received by editor(s): May 3, 2007
Published electronically: January 28, 2008
Additional Notes: The first author was supported in part by NSF grant DMS-0406346
The second author was supported in part by NSF grant DMS-0604735
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.