Let E be a holomorphic vector bundle on the n-dimensional complex projective space ℙn, n ≥ 2, of generic splitting type (a1,…, ar), a1 ≥ … ≥ar. Let, for some 1≤i≤r−1, ai − ai+1 = 1. Then the obstruction for the existence of a coherent subsheaf of type (a1,…, ai) can be interpreted as a "part" Pi (E) of the Penrose transform. We obtain that, for n≥3, the property "E does not contain a coherent subsheaf of generic splitting type (a1,…,ai)" is preserved under restriction to general hyperplanes. If aj − aj+1 = 1 for all j = 1,…, r − 1, then this property (fulfilled for j = 1,…, r−1) is equivalent to stability in the sense of Mumford and Takemoto.