About restricting 2-bundles on \(\mathbb{P}{}^ 3\) to planes (Q1191424)

In Math. Ann. 226, 125-150 (1977; Zbl 0332.32021), \textit{W. Barth} proved that if \(E\) and \(F\) are stable rank-2 vector bundles on \(\mathbb{P}_ n\), \(n\geq 4\) whose restrictions to general hyperplanes are isomorphic, then \(E\) and \(F\) are isomorphic and asked whether this is true also for \(n=3\). The present paper settles this problem affirmatively. It shows that if \(E\) and \(F\) are rank-2 vector bundles on projective 3-space over an algebraically closed field of characteristic 0 with \(E| H\cong F| H\) for general planes \(H\subset\mathbb{P}_ 3\), then \(E\cong F\). A generalization to reflexive sheaves on \(\mathbb{P}\) is also given, where there are 2 types of exceptions from this principle.