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Einstein four-manifolds with self-dual Weyl curvature of nonnegative determinant. (English) Zbl 1473.53072

Summary: We prove that simply connected Einstein four-manifolds of positive scalar curvature are conformally Kähler if and only if the determinant of the self-dual Weyl curvature is positive.

MSC:

53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
32Q20 Kähler-Einstein manifolds
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