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## Main Question or Discussion Point

A random question - Does the Riemman tensor and the covariant derivate commute?

a yes/no answer would suffice, but any explanation would be welcome:)

From the equations, it looks as though they do for flat metrics - but if we have other manifolds, it seems to me that the Christoffel symbols may be functions of different coordinates, and as such, might be affected by the covariant derivative.

a yes/no answer would suffice, but any explanation would be welcome:)

From the equations, it looks as though they do for flat metrics - but if we have other manifolds, it seems to me that the Christoffel symbols may be functions of different coordinates, and as such, might be affected by the covariant derivative.