Einstein four-manifolds with self-dual Weyl curvature of nonnegative determinant

Peng Wu

Einstein four-manifolds with self-dual Weyl curvature of nonnegative determinant

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arxiv 1903.11818 v2 pith:D23KGBTF submitted 2019-03-28 math.DG

Peng Wu This is my paper · ORCID

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keywords curvaturedeterminanteinsteinfour-manifoldspositiveself-dualweylahler

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We prove that simply connected Einstein four-manifolds of positive scalar curvature are conformally K\"ahler if and only if the determinant of the self-dual Weyl curvature is positive.

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Einstein Manifolds, Self-Dual Weyl Curvature, and Conformally Kaehler Geometry
math.DG 2019-08 accept novelty 6.0 of 10

A pointwise condition on self-dual Weyl curvature characterizes conformally Kähler, Einstein 4-manifolds as del Pezzo surfaces, with a new proof and generalizations.

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