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In this paper we prove that in a stationary axisymmetric SU(2)Einstein-Yang-Mills theory the most reasonable circularity conditions that canbe considered for the Yang-Mills fields imply in fact that the field is ofembedded Abelian type, or else that the metric is not asymptotically flat.Comment: 5 pages, RevTeX. To be published in Phys. Rev.

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