This is from Hughston and Tod, Ex 8.5. Please give me an idea how to start with this.

If $\mathcal{L}_V g_{ij} = 2\phi g_{ij}$ then prove that $$ \mathcal{L}_V\Gamma^{i}_{jk} = \phi_{,j}\delta^{i}_{k} + \phi_{,k}\delta^{i}_{j} - g_{jk}\phi^{,i}. $$

I was thinking we could expand the connection in terms of the metric and then use Liebniz but I don't think the Lie derivative would commute past the derivative on the metric.


closed as off-topic by ACuriousMind Mar 3 at 15:31

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "Homework-like questions should ask about a specific physics concept and show some effort to work through the problem. We want our questions to be useful to the broader community, and to future users. See our meta site for more guidance on how to edit your question to make it better" – ACuriousMind
If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ Please note that homework-like questions and check-my-work questions are generally considered off-topic here. We intend our questions to be potentially useful to a broader set of users than just the one asking, and prefer conceptual questions over those just asking for a specific computation. $\endgroup$ – ACuriousMind Mar 3 at 15:31