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

TL;DR

This paper derives integrability conditions for conformal and Killing-Yano tensors in all dimensions, linking their existence to the Weyl tensor, and explores their properties in Einstein and maximally symmetric spaces.

Contribution

It provides the first comprehensive derivation of integrability conditions for conformal Killing-Yano tensors in arbitrary dimensions, relating them to the Weyl tensor.

Findings

Integrability conditions expressed in terms of the Weyl tensor.

In Einstein spaces, conformal Killing-Yano tensors generate Killing-Yano tensors.

In maximally symmetric spaces, the covariant derivative of a Killing-Yano tensor is a closed conformal Killing-Yano tensor.

Abstract

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.