2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/51681The multi-centre metrics are a family of euclidean solutions of the empty space Einstein equations with self-dual curvature. For this full class, we determine which metrics do exhibit an extra conserved quantity quadraic in the momenta, induced by a Killing-Stackel tensor. Our results bring to light several metrics which correspond to classically integrable dynamical systems. They include, as particular cases, the Eguchi-Hanson and Taub-NUT metrics.Latex, 16 pages, 0 figureHigh Energy Physics - TheoryGeneral Relativity and Quantum Cosmologytext