# nLab Killing-Yano tensor

### Context

#### Riemannian geometry

Riemannian geometry

## Applications

#### Differential geometry

differential geometry

synthetic differential geometry

# Contents

## Definition

On a (pseudo-)Riemannian manifold $(X,g)$ a Killing-Yano tensor is a differential form $\omega$ such that

$\nabla_{(\mu} \omega_{\alpha_0), \alpha_1, \cdots , \alpha_n} = 0 \,,$

where $\nabla$ is the covariant derivative with respect to the Levi-Civita connection of $g$.

There is also a variant of conformal Killing-Yano tensors

(…)

## Properties

Killing-Yano tensors serve as “square roots” of Killing tensor. In a spacetime with a Killing tensor $H$ the relativistic particle has an extra conserved quantity. If it refines to a Killing-Yano tensor then also the spinning particle or superparticle has an extra odd conserved quantity. If $H = g$ then this is an extra worldline supersymmetry.

## Examples

The Kerr spacetime admits a conformal Killing-Yano tensor (…)

## References

For instance

• O. P. Santillan, Killing-Yano tensors and some applications (arXiv:1108.0149)

• Jacek Jezierski, Maciej Łukasik, Conformal Yano-Killing tensor for the Kerr metric and conserved quantities (arXiv:gr-qc/0510058)

• W. Dietz and R. Rüdiger, Space-Times Admitting Killing-Yano Tensors. I Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences Vol. 375, No. 1762 (Mar. 31, 1981), pp. 361 (JSTOR)

Revised on September 17, 2011 13:23:18 by Urs Schreiber (82.113.99.0)