2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59189We introduce the tangent space on a quantum hyperboloid. We define an action of this tangent space on the corresponding "quantum function space" ${\cal A}$, what converts the elements of the tangent space into "braided vector fields". The tangent space is shown to be a projective ${\cal A}$-module and we define a quantum (pseudo)metric and a quantum connection (partially defined) on it.30 pages, Latex. To appear in Cahiers de topologie et géométrie différentielle catégoriqueQuantum Algebratext