Géométrie de l'espace tangent sur l'hyperboloïde quantique

Abstract

We introduce the tangent space on a quantum hyperboloid. We define an action of this tangent space on the corresponding "quantum function space" $\mathcal{A}$, what converts the elements of the tangent space into "braided vector fields". The tangent space is shown to be a projective $\mathcal{A}$-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 catégorique