Definition:Killing Tensor
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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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