2013/10/01 by Rolf Soeren Krausshar, Krausshar, Rolf Soeren, Jürgen Tolksdorf +1
Mathematics · Physics and Astronomy · #30G35 #70S15 #Algebraic and Geometric Analysis #Black Holes and Theoretical Physics #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.CV #math.DG #msc:30G35 #msc:70S15
paper · pdf · doi:10.48550/arxiv.1310.0338
arxiv created 2013/10/01 · openalex publication_date 2013/10/01 · arxiv updated 2013/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we show how hypercomplex function theoretical objects can be used to construct explicitly self-dual SU(2)-Yang-Mills instanton solutions on certain classes of conformally flat 4-manifolds. We use a hypercomplex argument principle to establish a natural link between the fundamental solutions of D Δf = 0 and the second Chern class of the SU(2) principal bundles over these manifolds. The considered base manifolds of the bundles are not simply-connected, in general. Actually, this paper summarizes an extension of the corresponding results of Gürsey and Tze on a hyper-complex analytical description of SU(2) instantons. Furthermore, it provides an application of the recently introduced new classes of hypercomplex-analytic automorphic forms.