Einstein Metrics, Harmonic Forms, and Conformally Kaehler Geometry
Abstract
The author has elsewhere given a complete classification of those compact oriented Einstein 4-manifolds on which the self-dual Weyl curvature is everywhere positive in the direction of some self-dual harmonic 2-form. In this article, similar results are obtained when the self-dual Weyl curvature is everywhere non-negative in the direction of a self-dual harmonic 2-form that is transverse to the zero section of the bundle of self-dual 2-forms. However, this transversality condition plays an essential role in the story; dropping it leads one into wildly different territory where entirely different phenomena predominate.
Cite
@article{arxiv.1903.00956,
title = {Einstein Metrics, Harmonic Forms, and Conformally Kaehler Geometry},
author = {Claude LeBrun},
journal= {arXiv preprint arXiv:1903.00956},
year = {2019}
}
Comments
26 pages, LaTeX2e. This version strengthens several technical results, and modifies some key terminology in order to agree with standard conventions