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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]].

== Description ==

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.

== See also ==

* [[Mathematics]]
* [[Vector field]]

==  External links ==

* [https://en.wikipedia.org/wiki/Killing_vector_field Killing vector field] @ Wikipedia