Killing tensor

For $(X,g)$ a (pseudo-)Riemannian manifold a **Killing tensor** is a section of a symmetric power of the tangent bundle

$K \in Sym^k \Gamma(T X)$

which is covariantly constant in that

```
\nabla_{(\mu K_{\alpha_1, \cdots, \alpha_k}) = 0
\,.
```

For $k = 1$ this reduces to the notion of Killing vector.

For every Killing tensor $K$ on $(X,g)$ the dynamics of the relativistic particle on $X$ has a further conserved quantity. In the canonical case $K = g$ this quantity is the energy Hamiltonian of the particle.

The analog of this for spinning particles and superparticles are Killing-Yano tensors.

Created on September 17, 2011 11:12:16
by Urs Schreiber
(82.113.99.49)