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We study vacuum solutions of five-dimensional Einstein equations generated bythe inverse scattering method. We reproduce the black ring solution which wasfound by Emparan and Reall by taking the Euclidean Levi-Civita metric plusone-dimensional flat space as a seed. This transformation consists of twosuccessive processes; the first step is to perform the three-solitonictransformation of the Euclidean Levi-Civita metric with one-dimensional flatspace as a seed. The resulting metric is the Euclidean C-metric with extraone-dimensional flat space. The second is to perform the two-solitonictransformation by taking it as a new seed. Our result may serve as a steppingstone to find new exact solutions in higher dimensions.Comment: 12 pages, to be published in PR

Vacuum solutions of five dimensional Einstein equations generated byinverse scattering method. II. Production of the black ring solution