Curvature in the Balance: The Weyl Functional and Scalar Curvature of 4-Manifolds

2022/03/04 by Claude LeBrun, LeBrun, Claude · 1 citation
Mathematics · Physics and Astronomy · #53C18 #53C20 (primary) #57K43 #57R55 (secondary) #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2203.02528

openalex publication_date 2022/03/04 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

The infimum of the Weyl functional is shown to be surprisingly small on many compact 4-manifolds that admit positive-scalar-curvature metrics. Results are also proved that systematically compare the scalar and self-dual Weyl curvatures of certain almost-Kaehler 4-manifolds.

Cited by

• Weyl energy and connected sums of four-manifolds

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• Einstein Manifolds, Self-Dual Weyl Curvature, and Conformally Kaehler Geometry
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