2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/145271This is the first in a series of papers in which we develop a twistor-based method of constructing hyperkaehler metrics from holomorphic functions and elliptic curves. As an application, we revisit the Atiyah-Hitchin manifold and derive in an explicit holomorphic coordinate basis closed-form formulas for, among other things, the metric, the holomorphic symplectic form and all three Kaehler potentials.40 pages, 1 figureDifferential GeometryHigh Energy Physics - Theorytext