LeBrun, Claude Polarized 4-manifolds, extremal Kähler metrics, and Seiberg-Witten theory. (English) Zbl 0874.53051 Math. Res. Lett. 2, No. 5, 653-662 (1995). Author’s abstract: “ Using Seiberg-Witten theory, it is shown that any Kähler metric of constant negative scalar curvature on a compact 4-manifold \(M\) minimizes the \(L^2\)-norm of scalar curvature among Riemannian metrics compatible with a fixed decomposition \(H^2(M)=H^+\oplus H^-\). This implies, for example, that any such metric on a minimal ruled surface must be locally symmetric”. Reviewer: N.Blažić (Beograd) Cited in 2 ReviewsCited in 12 Documents MSC: 53C55 Global differential geometry of Hermitian and Kählerian manifolds 57N13 Topology of the Euclidean \(4\)-space, \(4\)-manifolds (MSC2010) 53C35 Differential geometry of symmetric spaces Keywords:Kähler metric; scalar curvature; Seiberg-Witten theory; locally symmetric space PDFBibTeX XMLCite \textit{C. LeBrun}, Math. Res. Lett. 2, No. 5, 653--662 (1995; Zbl 0874.53051) Full Text: DOI