Gravitational Instantons, Weyl Curvature, and Conformally Kaehler Geometry
Differential Geometry
2023-11-14 v2
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.
Keywords
Cite
@article{arxiv.2310.14387,
title = {Gravitational Instantons, Weyl Curvature, and Conformally Kaehler Geometry},
author = {Olivier Biquard and Paul Gauduchon and Claude LeBrun},
journal= {arXiv preprint arXiv:2310.14387},
year = {2023}
}
Comments
25 pages, LaTeX2e. Minor corrections. Many added references