Named for a physicist by the name of Killing, not for the type of action such a vector might take, a Killing vector is an important concept in General Relativity. It is a tangent vector to a trajectory along which the metric tensor is invariant. Taking the inner product of a Killing vector and a vector tangent to a geodesic produces a constant of motion.

The existence of a timelike Killing vector implies that the spacetime is stationary.