2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/120585We study a class of asymptotically cylindrical Ricci-flat Kähler metrics arising on quasiprojective manifolds. Using the Calabi--Yau geometry and analysis and the Kodaira--Kuranishi--Spencer theory and building up on results of N.Koiso for the case of compact manifolds, we show that under rather general hypotheses any `small' asymptotically cylindrical Ricci-flat deformations of asymptotically cylindrical Ricci-flat Kähler metrics are again Kähler, possibly with respect to a perturbed complex structure. We also find the dimension of the moduli space for these small deformations. In the class of asymptotically cylindrical Ricci-flat metrics on $2n$-manifolds, the holonomy reduction to SU(n) is an open condition.16 pagesDifferential Geometry14J32, 32Q25, 53C55text