Abstract
Neugebauer's results are doublized and the double complex transformations of the axisymmetric stationary vacuum field and the cylindrically symmetric vacuum field are obtained. Neugebauer's original results correspond to half of ours. By making use of these double Backlund transformations, we can construct a kind of double realization of the Geroch group. This cannot be achieved from Neugebauer's original results. Moreover, it is more general than Zhong's.
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