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I saw the following notation in a paper: $T_{ab;cd}$. Does this mean $\nabla_c\nabla_d T_{ab}$, or $\nabla_d\nabla_c T_{ab}$? I couldn't find a reference on a quick internet search.

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  • $\begingroup$ When I use similar notation, I always intend the latter expression. However, it’s difficult to answer your question precisely without knowing the conventions of the authors. $\endgroup$
    – MathIsArt
    Jul 30, 2022 at 17:36
  • $\begingroup$ I believe the latter is more common, but you can’t count on it. Whenever you read anything in differential geometry, you have to figure what notation conventions the author is using. I usually rewrite all the formulas using my own conventions. This implies you have to adopt your own set of conventions. $\endgroup$
    – Deane
    Jul 30, 2022 at 19:49

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