2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/185645We derive Bogomolny equations for an Einstein-Yang-Mills-dilaton-$σ$ model (EYMD-$σ$) on a static spacetime, showing that the Einstein equations are satisfied if and only if the associated (conformally scaled) three-metric is flat. These are precisely the static metrics for which super-covariantly constant spinors exist. We study some general properties of these equations and then consider the problem of obtaining axially symmetric solutions for the gauge group SU(2).24 pages LaTex, 1 Figure, revised text for publicationHigh Energy Physics - TheoryGeneral Relativity and Quantum Cosmologytext