In today's Relativity and Gravitation class, my prof was discussing about Riemann-Christoffel Tensor and he derived it. But in the end he told that there are many ways one can derive the Riemann Tensor. So i wonder how many ways it could be done and wish to learn them.

  • $\begingroup$ How did your professor derive it? $\endgroup$ – Rodney Dunning Sep 18 at 13:33
  • $\begingroup$ he did it using covariant derivatives $\endgroup$ – Ashwin Balaji Sep 18 at 15:32
  • $\begingroup$ See math.stackexchange.com/questions/2160940/…. There are also several sets of lecture notes that professors have shared online, many with step-by-step derivations. I found several good resources searching "how to derive the Riemann Tensor" on Google. $\endgroup$ – Rodney Dunning Sep 19 at 16:21
  • $\begingroup$ My purpose of asking this is this page will serve as a reference for all such derivations. $\endgroup$ – Ashwin Balaji Sep 20 at 23:25