The Einstein-Maxwell Equations, Kaehler Metrics, and Hermitian Geometry

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

References in corpus (3)

• On nodal sets for Dirac and Laplace operators
• Einstein Metrics on Complex Surfaces
• Ambitoric geometry I: Einstein metrics and extremal ambikaehler structures

Cited by in corpus (7)

• Kähler metrics with constant weighted scalar curvature and weighted K-stability
• The Einstein-Maxwell Equations and Conformally Kaehler Geometry
• Volume minimization and Conformally Kähler, Einstein-Maxwell geometry
• NUTs, Bolts, and Spindles
• Conformally Kähler, Einstein-Maxwell metrics on Hirzebruch surfaces
• Volume minimization and obstructions to solving some problems in Kähler geometry
• Einstein--Maxwell equations on 4-dimensional Lie algebras