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The relation between the SL(2,R)/SO(2)- and the SL(2,C)-chiral model thatnaturally arise within the metric respectively the Ashtekar formulation of twoKilling field reduced Einstein gravity is revealed. Both chiral models turn outto be completely equivalent even though the transition from the coset- to theSL(2,C)-model is accompanied by a disappearance of the non-ultralocal terms inthe Poisson brackets.Comment: 9 pages, LaTeX2

A comparison of metric and Ashtekar variables in two Killing field reduced gravity