The Einstein-Maxwell Equations and Conformally Kaehler Geometry

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 Kähler 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).

41 pages. LaTeX2e

References in corpus (1)

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

Cited by in corpus (5)

• Kähler metrics with constant weighted scalar curvature and weighted K-stability
• Metrics of Eguchi-Hanson types with the negative constant scalar curvature
• NUTs, Bolts, and Spindles
• Conformally Kähler, Einstein-Maxwell metrics on Hirzebruch surfaces
• Metrics of Horowitz-Myers type with the negative constant scalar curvature