Instability of conformally K\"ahler, Einstein metrics
Differential Geometry
2025-02-11 v3
Abstract
We prove the instability of conformally K\"ahler, 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 hyperK\"ahler and to the Chen-Lebrun-Weber metric in particular.
Keywords
Cite
@article{arxiv.2310.10109,
title = {Instability of conformally K\"ahler, Einstein metrics},
author = {Olivier Biquard and Tristan Ozuch},
journal= {arXiv preprint arXiv:2310.10109},
year = {2025}
}
Comments
An argument was missing for showing instability. This is now fixed