Abstract
Let $M$ be a smooth manifold of dimension $m>0$, and denote by $S_{\rm can}$ the canonical Nijenhuis tensor on $TM$. Let $\varPi $ be a Poisson bivector on $M$ and $\varPi ^{T}$ the complete lift of $\varPi $ on $TM$. In a previous paper, we have shown th
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