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 K¨ahler-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#2CP2 discovered in [8].