Definition:Killing Tensor

Definition
Let $\struct {M, g}$ be a Riemannian manifold.

Let $K$ be a symmetric tensor field of type $\paren {p, 0}$ with components $K_{\mu_1 \ldots \mu_p}$.

Let $\nabla$ be the covariant derivative.

Then $K$ is called the Killing tensor (of order $p$) if:


 * $\nabla_{(\alpha} K_{\mu_1 \ldots \mu_p)} = 0$

where $\paren {\ldots}$ denotes the tensor symmetrization.