Rank-two weak Fano bundles on a four-dimensional quadric hypersurface Q 4

We classify rank 2 weak Fano bundles on a four-dimensional smooth quadric hypersurface [Formula: see text]. Up to twisting with a line bundle, such a bundle is either a split bundle, a spinor bundle, or one of the stable bundles with Chern classes [Formula: see text] = –1 and [Formula: see text] = (1, 1) constructed in [APW94].