2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/150054We introduce equations for special metrics, and notions of stability for some new types of augmented holomorphic bundles. These new examples include holomorphic extensions, and in this case we prove a Hitchin-Kobayashi correspondence between a certain deformation of the Hermitian-Einstein equations and our definition of stability for an extension.contact authors at bradlow@uiuc.edu or OGPRADA@ccuam3.sdi.uam.es, AMSTeX v2.1Algebraic Geometrytext