2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/111608If the conformal holonomy group $Hol(\mathcal{T})$ of a simply connected space with conformal structure of signature $(2p-1,2q-1)$ is reduced to $\U(p,q)$ then the conformal holonomy is already contained in the special unitary group $\SU(p,q)$. We present two different proofs of this statement, one using conformal tractor calculus and an alternative proof using Sparling's characterisation of Fefferman metrics.14 pagesDifferential Geometry53A30, 53C29; 32V05; 53B30; 53C07text