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Apr 29, 2020 at 19:20 comment added G. Smith Your previous questions indicate that you have just started to study differential geometry, so I find it somewhat... surprising!... that you are using a connection with torsion. Please ignore my answer. It is the right answer for the other 99.99% of readers.
Apr 29, 2020 at 18:05 comment added Nothing Oh that is the problem, I'm not using levi civita conecction. I know that in $\nabla_{a}g_{bc}=0$ when torsion is $0$.
Apr 29, 2020 at 17:15 history edited G. Smith CC BY-SA 4.0
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Apr 29, 2020 at 17:00 history edited G. Smith CC BY-SA 4.0
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Apr 29, 2020 at 16:51 history answered G. Smith CC BY-SA 4.0