2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/56592We study the anti-self-dual equation for non-diagonal SU(2)-invariant metrics and give an equivalent ninth-order system. This system reduce to a sixth-order system if the metric is in the conformal class of scalar-flat-Kaehler metric.9 pages, LaTeXMathematical PhysicsDifferential Geometry53C25(Primary), 53C80, 83C20(Secondary)text