A classical result by Horrocks characterizes the vector bundles without intermediate co- homology on a projective space as direct sum of line bundles. A very simple proof of this criterion use the Castelnuovo-Mumford regularity. Arrondo and Gra~na generalized Horrocks criterion by giving a cohomological characterization of the universal bundles on G(1; 4). In this talk we introduce a notion of regularity for coherent sheaves on Grassmannians of lines. We use this notion in order to prove a cohomological characterization of exterior and sym- metric powers of the universal bundles on every G(1; n). Moreover we discuss some problems related to monads and splitting criteria on quadric hypersurfaces.