Talk:Cotton tensor

External links modified (January 2018)

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Making the definition readable by non-experts

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 $\nabla _{j}$ refer to the connection (covariant derivative) associated to g (and w.r.t. the vector field $X=\partial _{j}=\partial /\partial x^{j}$) or is it just the partial derivative w.r.t. j?
• Does $\nabla _{j}\mathrm {Ric} _{ij}$ mean $(\nabla _{j}\mathrm {Ric} )_{ij}$ or $\nabla _{j}(\mathrm {Ric} _{ij})$? This is related to the previous question.
• Similarly the absence of parentheses in $\nabla _{j}Rg_{ik}$ makes it ambiguous, and as a non-expert, I cannot guess which parenthesing (bracketing) was meant: $(\nabla _{j}(Rg))_{ik}$, $\nabla _{j}(Rg_{ik})$, $(\nabla _{j}R)g_{ik}$, maybe another one I would have missed?

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