  From the metric and one Killing-Yano tensor of rank D-2 in any D-dimensional
spacetime with such a principal Killing-Yano tensor, we show how to generate
k=[(D+1)/2] Killing-Yano tensors, of rank D-2j for all j=0,...,k-1, and k
rank-2 Killing tensors, giving k constants of geodesic motion that are in
involution. For the example of the Kerr-NUT-AdS spacetime (hep-th/0604125) with
its principal Killing-Yano tensor (gr-qc/0610144), these constants and the
constants from the k Killing vectors give D independent constants in
involution, making the geodesic motion completely integrable (hep-th/0611083).
The constants of motion are also related to the constants recently obtained in
the separation of the Hamilton-Jacobi and Klein-Gordon equations
(hep-th/0611245).
