The Einstein-Maxwell Equations, Kaehler Metrics, and Hermitian Geometry
Differential Geometry
2015-05-20 v2
Abstract
Any constant-scalar-curvature Kaehler (cscK) metric on a complex surface may be viewed as a solution of the Einstein-Maxwell equations, and this allows one to produce solutions of these equations on any 4-manifold that arises as a compact complex surface with b_1 even. It is shown, however, that not all solutions of the Einstein-Maxwell equations on such manifolds arise in this way; new examples can be constructed by means of conformally Kaehler geometry.
Cite
@article{arxiv.1411.3992,
title = {The Einstein-Maxwell Equations, Kaehler Metrics, and Hermitian Geometry},
author = {Claude LeBrun},
journal= {arXiv preprint arXiv:1411.3992},
year = {2015}
}
Comments
19 pages; 1 figure. With added references, improved notation, and many minor corrections. To appear in special issue of the Journal of Geometry and Physics