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We derive a generalization of the flat space Yang's and Newman's equationsfor self-dual Yang-Mills fields to (locally) conformally Kahler Riemannian4-manifolds. The results also apply to Einstein metrics (whose full curvatureis not necessarily self-dual). We analyse the possibility of hidden symmetriesin the form of Backlund transformations, and we find a continuous group ofhidden symmetries only for the case in which the geometry is conformallyhalf-flat. No isometries are assumed.

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