The Einstein-Maxwell Equations, Kaehler Metrics, and Hermitian Geometry
arXiv:1411.3992 · doi:10.1016/j.geomphys.2015.01.009
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.
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