The Geometry of 4-Manifolds: Curvature in the Balance
speaker: Claude LeBrun (Stony Brook University)abstract: 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 these lectures, 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.
timetable:
Wed 8 Jun, 11:00 - 11:45, Aula Dini
Wed 8 Jun, 11:45 - 12:30, Aula Dini
Thu 9 Jun, 9:00 - 9:45, Aula Dini
Thu 9 Jun, 9:45 - 10:30, Aula Dini
Fri 10 Jun, 9:00 - 9:45, Aula Dini
Fri 10 Jun, 9:45 - 10:30, Aula Dini
documents:
The Geometry of 4-Manifolds: Curvature in the Balance PART 1
The Geometry of 4-Manifolds: Curvature in the Balance PART 2
The Geometry of 4-Manifolds: Curvature in the Balance PART 3
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