Lifts of Poisson–Nijenhuis Structures to Weil Bundles

In the present paper we show that the complete lifts of the structure tensors $P$ and $N$ of a Poisson–Nijenhuis manifold $(M,P,N)$ to the Weil bundle $T^\mathbb AM$ induce a structure of Poisson–Nijenhuis manifold on $T^\mathbb AM$. We compute the modular vector fields of this manifold.