# Sources about Killing vector fields?

• Topology
Mentor

## Main Question or Discussion Point

I'm interested in Killing vector fields and want to ask whether anybody can name me a good textbook or online-source about them, preferably with a general treatment with local coordinates as examples and not at the center of consideration.

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George Jones
Staff Emeritus
Starting on page 83, "Differential Geometry and Lie Groups for Physicists", by Fecko, has my favourite treatment of Killing vectors. It has lots of great examples in its short exrecises. I am not sure if has enough coordinate-invariant stuff for your tastes, but it does start with the definition $\mathcal{L}_\xi g = 0$, where $\mathcal{L}$ is the Lie derivative and the vector field $\xi$ is generated by a one-parameter group of isometries.