Instanton sheaves on ruled Fano 3-folds of Picard rank 2 and index 1

We study rank 2 h-instanton sheaves on projective threefolds. We demonstrate that any orientable rank 2, non-locally free h-instanton sheaf with defect 0 on a threefold can be obtained as an elementary transformation of a locally free h-instanton sheaf. Our focus then shifts to ruled Fano threefolds of Picard rank 2 and index 1, of which there are five deformation classes. We establish the existence of orientable rank 2 h-instanton bundles on such varieties. Additionally, we prove the existence of Ulrich bundles on such varieties, which correspond to h-instanton sheaves of minimum charge.