On self-dual Yang–Mills fields on special complex surfaces

We derive a generalization of the flat space Yang's and Newman's equations for self-dual Yang-Mills fields to (locally) conformally Kahler Riemannian 4-manifolds. The results also apply Einstein metrics (whose full curvature is not necessarily self-dual). analyse possibility hidden symmetries in form Backlund transformations, we find continuous group only case which geometry half-flat. No isometries are assumed.