Category:Definitions/Killing Vector Fields

This category contains definitions related to Killing Vector Fields.
Related results can be found in Category:Killing Vector Fields.

Let $\struct {M, g}$ be a Riemannian manifold.

Let $\map {\mathfrak X} M$ be the space of smooth vector fields of $M$.

Let $X \in \map {\mathfrak X} M$.

Let $\LL$ be the Lie derivative.

Suppose $\map {\LL_X} g = 0$.

Then $X$ is called the Killing vector field.