2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/139291We give an explicit description of rational curves in the product of three copies of complex projective lines, which are transformed into twistor lines in M. Nagata's example of non-projective complete algebraic variety, viewed as the twistor space of Eguchi-Hanson metric. In particular, we show that there exist two families of such curves and both of them are parameterized by mutually diffeomorphic, connected real 4-dimensional manifolds. We also give a relationship between these two families through a birational transformation naturally associated to the Nagata's example.V2: 10 pages, 1 figure; a figure explaining key fact added, comments on automorphism group added. Accepted for publication in J. Math. Kyoto UnivDifferential GeometryAlgebraic Geometrytext