I want to show this equation of the Lie-derivative:
whereas L_X is the Lie derivative and X,Y are vector fields.
I try to understand the equation, but i'm hopelessly.
Can you help me by my task.
How do you define the Lie derivative? For any of the (equivalent) definitions, Lie derivative has the property that it commutes with contraction. And is the contraction of Y and .
Let denote the contraction , we have
commutes with contraction =
Leibniz rule =
perform contraction =