Moduli spaces of Ulrich bundles on the Fano 3-fold $V_5$

We study moduli spaces of Ulrich bundles of rank $r \geq 2$ on the Fano 3-fold $V_5$ of Picard number 1, degree 5 and index 2. We prove that the moduli space of stable Ulrich bundles of rank $r$ on $V_5$ can be identified with a smooth $(r^2+1)$-dimensional open subset of the moduli space of stable quiver representations with dimension vector $(r, r)$ of the Kronecker quiver with 2 vertices and 3 arrows.