Stationary axisymmetric SU(2) Einstein-Yang-Mills fields with restricted circularity conditions are Abelian

In this paper we prove that in a stationary axisymmetric SU(2) Einstein-Yang-Mills theory the most reasonable circularity conditions that can be considered for the Yang-Mills fields imply in fact that the field is of embedded Abelian type, or else that the metric is not asymptotically flat.