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We give a systematic local description of invariant metrics and otherinvariant fields on a spacetime under the action of a (non-abelian) group. Thisincludes the invariant fields in a neighbourhood of a principal and a specialorbit. The construction is illustrated with examples. We also apply theformalism to give the R-symmetry invariant metrics of some AdS backgrounds andcomment on applications to Kaluza-Klein theory.

Symmetries, a systematic construction of invariant fields and AdS backgrounds