On the restriction of vector bundles to good families of curves

Summary Here we study the restriction to suitable curves of certain vector bundles on projective varieties. We handle in particular: (a) the descent of a vector bundle for the contraction of an extremal ray on a smooth 3-fold (using Mori theory); (b) the stability or semistability (in any characteristic) of certain homogeneus vector bundles on Pⁿ and their restriction to suitable subvarieties.