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In this paper we show how hypercomplex function theoretical objects can beused to construct explicitly self-dual SU(2)-Yang-Mills instanton solutions oncertain classes of conformally flat 4-manifolds. We use a hypercomplex argumentprinciple to establish a natural link between the fundamental solutions of $D\Delta f = 0$ and the second Chern class of the SU(2) principal bundles overthese manifolds. The considered base manifolds of the bundles are notsimply-connected, in general. Actually, this paper summarizes an extension ofthe corresponding results of G\"ursey and Tze on a hyper-complex analyticaldescription of SU(2) instantons. Furthermore, it provides an application of therecently introduced new classes of hypercomplex-analytic automorphic forms.

Applications of hypercomplex automorphic forms in Yang-Mills gauge theories