Instability of conformally Kähler, Einstein metrics
arXiv:2310.10109
Abstract
We prove the instability of conformally Kähler, compact or ALF Einstein 4-manifolds with nonnegative scalar curvature which are not half conformally flat. This applies to all the known examples of gravitational instantons which are not hyperKähler and to the Chen-Lebrun-Weber metric in particular.
An argument was missing for showing instability. This is now fixed