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:
“Instead of killing and dying in order to produce the being that we are not, we have to live and let live in order to create what we are.”
—Albert Camus (1913–1960)
“I see a girl dragged by the wrists
Across a dazzling field of snow,
And there is nothing in me that resists.
Once it would not be so....”
—Philip Larkin (1922–1986)