Killing vector field

In mathematics and theoretical physics, a Killing vector field or Killing field (named after Wilhelm Killing) is a vector field on a Riemannian manifold or pseudo-Riemannian manifold that preserves the metric.

Flows generated by Killing vector fields are continuous isometries of the manifold. This means that the flow generates a symmetry, in the sense that moving each point of an object the same distance in the direction of the Killing vector will not distort distances on the object.