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math.DG2010
Einstein Manifolds and Extremal Kahler Metrics
Claude LeBrun
In joint work with Chen and Weber, the author has elsewhere shown that CP2#2(-CP2) admits an Einstein metric. The present paper gives a new and rather different proof of this fact.…
math.DG2010
On Einstein, Hermitian 4-Manifolds
Claude LeBrun
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 e…