KillingVectorOf is an option for DefTensor that determines whether the defined tensor is a Killing vector of a metric. |

- KillingVectorOf is used as DefTensor[tensor, manifold, KillingVectorOf→ metric].

- A vector is a Killing vector of the metric if .

- Lie derivatives of the metric with respect to the Killing vector are automatically zero.

- The covariant derivative of the Killing vector is automatically antisymmetric in the two free indices.

- The second derivative of the Killing vector is automatically converted to a contraction of the Riemann tensor with the Killing vector.

- The Killing vector must be a vector (that is, have one tangent bundle index), but can have one or more label indices.