Talk:Cotton tensor

Latest comment: 3 years ago by Arnaud Chéritat in topic Making the definition readable by non-experts
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Making the definition readable by non-experts

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I have read part of Berger Gauduchon Mazet long time ago and remember a few things about connections and the curvature tensor, and conventions in this field, but not all. The expression given for the coefficients of the Cotton tensor appears ambiguous to me.

  • Does   refer to the connection (covariant derivative) associated to g (and w.r.t. the vector field  ) or is it just the partial derivative w.r.t. j?
  • Does   mean   or  ? This is related to the previous question.
  • Similarly the absence of parentheses in   makes it ambiguous, and as a non-expert, I cannot guess which parenthesing (bracketing) was meant:  ,  ,  , maybe another one I would have missed?

Arnaud Chéritat (talk) 10:04, 24 June 2021 (UTC)Reply