- expr - any expression (on which Lie derivative is defined). v1, v2, v3..., vn - vector fields.
- The derivative has the following properties:
- - For any vector fields X1, X2, .., Xn and expression a we have: LX1, X2, .., Xn(a)=LX1(LX2(..LXn(a)))
- - For any vector field X and 0-form f we have: Lx(f)=X(d(f))
- - For vector fields X and Y we have: Lx(Y)=[X, Y]
- - For any vector field X and tensor fields and T the Leibniz rule for the Lie derivative takes place: LX(T)=(LX())T+(LX(T))
- - For any vector field X and p-form we have: LX()=X(d())+d(X())
Basic Examples (1)