The Geometry of 4-Manifolds: Curvature in the Balance

by Claude LeBrun (Stony Brook University)

Monday May 26, 2025, 2:00 PM → 3:00 PM Europe/Paris

Salle Pellos (1R2-207)

For Kaehler metrics on a compact complex surface, the L2-norms of the scalar curvature and the self-dual Weyl curvature are equal, up to a universal multiplicative constant. By contrast, when considered as functionals on the space of all Riemannian metrics on a fixed compact oriented 4-manifold, these two L2-norms are completely independent. However, striking patterns emerge when we compare their sizes for special classes of Riemannian metrics, such as Einstein metrics or almost-Kaehler metrics. In this lecture, I will describe a number of results that establish such general patterns. I will then show how results from Kaehler geometry can be used to shed new light on the infimum of the Weyl functional.