On Optimal 4-Dimensional Metrics

2007/11/11 by Claude LeBrun, LeBrun, Claude, Bernard Maskit +1 · 1 citation
Computer Science · Mathematics · #30F40 #53C25 #Complex Variables (math.CV) #Computational Geometry and Mesh Generation #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.CV #math.DG #msc:30F40 #msc:53C25

paper · pdf · doi:10.48550/arxiv.0711.1668

37 pages, 5 figures

arxiv created 2007/11/11 · openalex publication_date 2007/11/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We completely determine, up to homeomorphism, which simply connected compact oriented 4-manifolds admit scalar-flat, anti-self-dual Riemannian metrics. The key new ingredient is a proof that the connected sum of five reverse-oriented complex projective planes admits such metrics.

Cited by

• Scalar Curvature in Dimension 4

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• Curvature Functionals, Optimal Metrics, and the Differential Topology of 4-Manifolds
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• Geography of 4-manifolds with positive scalar curvature