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.

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Source of Name

This entry was named for Wilhelm Karl Joseph Killing.

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