Compact Kähler surfaces with harmonic anti-self-dual Weyl tensor.
The author proves the following theorem: Let \((M, g, J)\) be a compact Kähler surface with harmonic anti-self-dual Weyl tensor \((\delta W^-=0)\). Then \(M\) has constant scalar curvature (and thus is Einstein or is locally a product of two Riemannian surfaces with constant sectional curvature) or is a ruled surface with extremal Kähler metric with non-constant scalar curvature which admits an opposite Hermitian structure \(\overline J\) such that \((M, g,\overline J)\) satisfies a \((G_2)\) condition of Gray and is conformal to an extremal Kähler surface.
scientific article; zbMATH DE number 1780874
scientific article