Gravitational Instantons, Weyl Curvature, and Conformally Kahler Geometry

Claude LeBrun, Stony Brook University
Fine Hall 314

This talk will describe my recent joint work 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 previously-classified solutions.