Solitonic generation of the five-dimensional black ring solution

Using the solitonic solution-generating technique, we rederived the one-rotational five-dimensional black ring solution found by Emparan and Reall. The seed solution is not the Minkowski metric, which is the seed of the $S^2$-rotating black ring. The obtained solution has more parameters than Emparan and Reall’s $S^1$-rotating black ring. We found the conditions of parameters to reduce the solution to the $S^1$-rotating black ring. In addition, we examined the relation between the expressions of the metric in the prolate-spheroidal coordinates and in the canonical coordinates.