2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152061We consider compact complex surfaces with Hermitian metrics which are Einstein but not Kaehler. It is shown that the manifold must be CP2 blown up at 1,2, or 3 points, and the isometry group of the metric must contain a 2-torus. Thus the Page metric on CP2#(-CP2) is almost the only metric of this type.latex, 2 figuresDifferential Geometrytext