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Past events in this series


Fri, 24 Oct 2025
12:00
L3

Gravitational Instantons, Weyl Curvature, and Conformally Kaehler Geometry

Claude LeBrun
(SUNY at Stony Brook)
Abstract

In this talk, I will discuss my joint paper with Olivier Biquard and Paul Gauduchon on ALF Ricci-flat Riemannian  4-manifolds. My collaborators had previously classified all such spaces that are toric and Hermitian, but not Kaehler. Our main result uses an open curvature condition to prove a rigidity result of the following type: any Ricci-flat metric that is sufficiently close to a non-Kaehler, toric, Hermitian ALF solution (with respect to a norm that imposes reasonable fall-off at infinity) is actually  one of the  known Hermitian toric  solutions.