Einstein Hermitian metrics of positive sectional curvature

Koca, Caner

doi:10.1090/S0002-9939-2014-11929-0

Einstein Hermitian metrics of positive sectional curvature
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Proc. Amer. Math. Soc. 142 (2014), 2119-2122 Request permission

Abstract:

It is shown that, up to scaling and isometry, the only complete 4-manifold with an Einstein metric of positive sectional curvature which is also Hermitian with respect to some complex structure is the complex projective plane $\mathbb {CP}_2$, equipped with its Fubini-Study metric.

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