2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/156498We show that Horrocks' criterion for the splitting of rank two vector bundles in P^3 can be extended, with some assumptions on the Chern classes, on non singular hypersurfaces in P^4. Extension of other splitting criterion are studied.Typesetting minor corrections madeAlgebraic Geometry14F05A splitting criterion for rank 2 vector bundles on hypersurfaces in P^4text