Cartan's magic formula states:
$$\mathcal{L}_v\omega = i_v\mathrm{d}\omega + \mathrm{d}i_v\omega$$
Is this also true for time dependent vector fields? If so: How can I prove it? If not: Is there a simple counter-example?
Thanks in advance!
Asked
Active
Viewed 448 times
1
-
1I guess I'm not quite sure what you mean. We can apply Cartan's formula on $M\times\mathbb R$, interpreting the vector field and $\omega$ as lifted. – Ted Shifrin May 11 '13 at 19:21
-
How do you define the Lie derivative of a time-independent vector field? – Chris Z May 26 '16 at 15:43