- #26

- 12

- 0

I stand with you with the demonstration but I think you should use the definition of the Lie derivative by including the flow map instead of p in the first term of the numerator (and similarly in the following lines):...

##(\mathcal L_XY)_p =\lim_{t\to 0}\frac{((\phi_{-t})_*Y)_p-Y_p}{t}##...

##(\mathcal L_XY)_p =\lim_{t\to 0}\frac{((\phi_{-t})_*Y)_ {\phi_t(p)}-Y_p}{t}\\##

and make use of the definition of the flow map:

##\phi_{t}^{-1}=\phi_{-t}## (together with ##\phi_{t}\circ\phi_{s}=\phi_{t+s}## and ##\phi_{0}=id##)