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arXiv · 1504.06669

The Einstein-Maxwell Equations and Conformally Kaehler Geometry

Claude LeBrun
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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).

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Claude LeBrun. 2015-04-24. The Einstein-Maxwell Equations and Conformally Kaehler Geometry. https://doi.org/10.1007/s00220-015-2568-5

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