English

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