Category:Killing Vector Fields
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This category contains results about Killing Vector Fields.
Definitions specific to this category can be found in Definitions/Killing Vector Fields.
Let $\struct {M, g}$ be a Riemannian manifold.
Let $\map {\mathfrak X} M$ be the space of smooth vector fields of $M$.
Let $X \in \map {\mathfrak X} M$.
Let $\LL$ be the Lie derivative.
Suppose $\map {\LL_X} g = 0$.
Then $X$ is called the Killing vector field.
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