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The Einstein-Maxwell Equations and Conformally Kaehler Geometry (1504.06669v1)
Published 24 Apr 2015 in math.DG
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 K\"ahler 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 S2 x S2 and CP_2 # (-CP_2).
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