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arXiv · 1406.3069

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

Carlos Batista
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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.

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Carlos Batista. 2015-01-14. Integrability Conditions for Killing-Yano Tensors and Conformal Killing-Yano Tensors. https://doi.org/10.1103/physrevd.91.024013

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