The <Lie bracket of vector fields> is the commutator of the corresponding derivations:
$$
[X,Y]f=X(Yf)-Y(Xf).
$$
For $X=X^i\partial_i$ and $Y=Y^i\partial_i$,
$$
\boxed{[X,Y]=\left(X^i\partial_iY^k-Y^i\partial_iX^k\right)\partial_k.}
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 115 / 2 / e / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/iii/paper-115/2/e/solution