2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/164661We prove that evolution families on complex complete hyperbolic manifolds are in one to one correspondence with certain semicomplete non-autonomous holomorphic vector fields, providing the solution to a very general Loewner type differential equation on manifolds.15 pagesComplex VariablesClassical Analysis and ODEs34M45; 32Q45; 32W99text