The Einstein-Maxwell Equations and Conformally Kaehler Geometry
Differential Geometry
2016-03-23 v1
Abstract
Page's Einstein metric on CP_2 # (-CP_2) is conformally related to an extremal Kaehler metric. Here we construct a family of conformally K\"ahler solutions of the Einstein-Maxwell equations that deforms the Page metric, while sweeping out the entire Kaehler cone of CP_2 # (-CP_2).The same method also yields analogous solutions on every Hirzebruch surface. This allows us to display infinitely many geometrically distinct families of solutions of the Einstein-Maxwell equations on the smooth 4-manifolds S^2 x S^2 and CP_2 # (-CP_2).
Cite
@article{arxiv.1504.06669,
title = {The Einstein-Maxwell Equations and Conformally Kaehler Geometry},
author = {Claude LeBrun},
journal= {arXiv preprint arXiv:1504.06669},
year = {2016}
}
Comments
41 pages. LaTeX2e