On Einstein, Hermitian 4-Manifolds

2010/10/01 by LeBrun, Claude · 1 citation
#14M25 #35B44 (Secondary) #53C25 #53C55 (Primary) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1010.0238

Abstract

Let (M,h) be a compact 4-dimensional Einstein manifold, and suppose that h is Hermitian with respect to some complex structure J on M. Then either (M,J,h) is Kaehler-Einstein, or else, up to rescaling and isometry, it is one of the following two exceptions: the Page metric on CP2 # (-CP2), or the Einstein metric on CP2 # 2 (-CP2) constructed in Chen-LeBrun-Weber.

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