We show that the GJMS operators of a special Einstein product factor as a composition of second- and fourth-order differential operators. In particular, our formula applies to the Riemannian product $H^{ \ell} \times S^{ d-\ell}$. We also show that there is an integer $D = D(k,\ell)$ such that if $d \geq D$, then for any special Einstein product $N^\ell \times M^{ d-\ell}$, the Green's function for the GJMS operator of order $2k$ is positive. As a result, these products give new examples of closed Riemannian manifolds for which the $Q_{ 2k}$-Yamabe problem is solvable.
Categories: math.DG math.AP