1. Gravitational Instantons, Weyl Curvature, and Conformally Kaehler Geometry
- Author
-
Biquard, Olivier, Gauduchon, Paul, and LeBrun, Claude
- Subjects
Mathematics - Differential Geometry ,53C25 (primary), 53C55, 83C20 (secondary) - Abstract
In a previous paper, the first two authors classified complete Ricci-flat ALF Riemannian 4-manifolds that are toric and Hermitian, but non-Kaehler. In this article, we consider general Ricci-flat deformations of such spaces, assuming only suitable fall-off conditions. Quite generally, we are able to show that such a deformation must be Hermitian, and must carry a non-trivial Killing vector field with fixed asymptotics. With mild additional hypotheses, we are then able to show that the new Ricci-flat metric must in fact belong to the family of previously classified metrics., Comment: 25 pages, LaTeX2e. Minor corrections. Many added references
- Published
- 2023