A fully nonlinear "Generalised Monge-Ampère" PDE on a torus

Abstract: We prove an existence result for a "generalised" Monge-Amp`ere equation introduced earlier under some assumptions on a flat complex 3-torus. As an application we prove the existence of Chern connections on certain kinds of holomorphic vector bundles on complex 3-tori whose top Chern character forms are given representatives.