Wow, this is a pretty spectacular post! I'm going to read it in a bit cause I currently have an assignment on, but thanks so much for putting the effort in to answer my question in such detail 🙏🙏
Oh, I wasn't aware, thanks for the comment, I'll make sure to be more careful in the future. But yes the problem is meant to be for an arbitrary connection, not specifically for the Levi-Civita connection.
Hi, thanks for the help; though I was under the impression that this only applied in some cases, like for the connection coefficients of the Levi-Civita connection, but not in every case.
Hi, thanks a lot,
I thought the error might be there, although I'm really new to this area could you explain what you mean by a second order operator? Do you mean something like ##\frac{\partial^2}{\partial x^i\partial x^j}##?
Alright, yeah, I've never used Latex before so it might take a while but I'll give it a go, you mean the example calculation right? Thanks for the link btw.
Hi,
I've been doing a course on Tensor calculus by Eigenchris and I've come across this problem where depending on the way I compute/expand the Lie bracket the Torsion tensor always goes to zero. If you have any suggestions please reply, I've had this problem for months and I'm desperate to...