Stable Ulrich bundles on Fano threefolds with Picard number 2

In this paper, we consider the existence problem of rank one and two stable Ulrich bundles on imprimitive Fano 3-folds obtained by blowing-up one of P3, Q (smooth quadric in P4), V3 (smooth cubic in P4) or V4 (complete intersection of two quadrics in P5) along a smooth irreducible curve. We prove that the only class which admits Ulrich line bundles is the one obtained by blowing up a genus 3, degree 6 curve in P3. Also, we prove that there exist stable rank two Ulrich bundles with c1=3H on a generic member of this deformation class.