Ulrich bundles on the degree six Segre fourfold

We study the resolution of an Ulrich bundle of arbitrary rank on the Segre fourfold $PP^2timesPP^2$. We characterize the Ulrich bundles $Vv$ of arbitrary rank on $PP^2timesPP^2$ with $h^1(VvotimesOmegaboxtimesOmega)=0$ or with $h^1(VvotimesOmega(-1)boxtimesOmega(-1))=0$ or obtained as pullback from $PP^2$ and we construct more complicated examples.