In mathematics, a Killing vector field (often just Killing field), named after Wilhelm Killing, is a vector field on a Riemannian manifold (or pseudo-Riemannian manifold) that preserves the metric. Killing fields are the infinitesimal generators of isometries; that is, flows generated by Killing fields are continuous isometries of the manifold. More simply, the flow generates a symmetry, in the sense that moving each point on an object the same distance in the direction of the Killing vector field will not distort distances on the object.
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Famous quotes containing the words killing and/or field:
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I know at thirty-three that one must shoot
As often as one gets the rare chance—
In killing there is more than commentary.”
—Allen Tate (1899–1979)
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—Sarah Fielding (1710–1768)