Integrability Conditions for Killing-Yano Tensors and Conformal Killing-Yano Tensors

摘要

The integrability conditions for the existence of a conformal Killing-Yanotensor of arbitrary order are worked out in all dimensions and expressed interms of the Weyl tensor. As a consequence, the integrability conditions forthe existence of a Killing-Yano tensor are also obtained. By means of suchconditions, it is shown that in certain Einstein spaces one can use a conformalKilling-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 covariantderivative of a Killing-Yano tensor is a closed conformal Killing-Yano tensorand that every conformal Killing-Yano tensor is uniquely decomposed as the sumof a Killing-Yano tensor and a closed conformal Killing-Yano tensor.