2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/163510In this note we take some initial steps in the investigation of a fourth order analogue of the Yamabe problem in conformal geometry. The Paneitz constants and the Paneitz invariants considered are believed to be very helpful to understand the topology of the underlined manifolds. We calculate how those quantities change, analogous to how the Yamabe constants and the Yamabe invariants do, under the connected sum operations.15 pagesDifferential GeometryGeneral TopologyGeometric Topology58J99, 53C99text