X.Calculating the Lie Derivative of a One-Form with Respect to a Vector Field

[rick1138]

I'd like an example of calculating the Lie derivative of a one-form with respect to a vector field, for example, the one-form

<br /> \omega = 3 dx_1 + 4x dx_2<br />

with the vector field

<br /> X = 7x \frac{\partial }{\partial x_1} + 2 \frac{\partial }{\partial x_2} <br />

Any input would be appreciated.

 

[matness]

i am also one waiting for a reply to this post
i have the formula to compute lie derivatives of one forms but not enough self-confidence to give an exact soln .actually i also did not understand which x do you talk about when saying 4xdx_2
i think here in this forum people have enough knowledge to answer but i could not understand why there is no reply .Is it too simple to answer?

 

[Mulder]

^No, it doesn't make any sense until an index is put on the "x" in the vector and the 1-form. After that, as you say, just use your formula for Lw