The integrability conditions for the existence of a conformal Killing–Yano tensor of arbitrary order are worked out in all dimensions and expressed in terms of the Weyl tensor. As a consequence, the integrability conditions for the existence of a Killing–Yano tensor are also obtained. By means of such conditions, it is shown that in certain Einstein spaces one can use a conformal Killing–Yano tensor of order $p$ to generate a Killing–Yano tensor of order $(p-1)$. Finally, it is proved that in maximally symmetric spaces the covariant derivative of a Killing–Yano tensor is a closed conformal Killing–Yano tensor and that every conformal Killing–Yano tensor is uniquely decomposed as the sum of a Killing–Yano tensor and a closed conformal Killing–Yano tensor.

• Received 31 October 2014

DOI:https://doi.org/10.1103/PhysRevD.91.024013