Talk:Coordinate Representation of Divergence

Latest changes
Latest change involving $g$ is not an error, but just a change of notation. The determinant of metric tensor is often denoted by $g$. In my source, however, $g$ denotes the metric tensor without explicitly presenting the local basis, that is, $g = g_{\mu\nu} \d x^\mu \otimes \d x^\nu$. Then the determinant of $g$ is written as $\det g = \map \det {g_{\mu \nu}}$. The rest of proof seems fine, but one still needs to link it properly. Also, I believe that I used a different symbol for the inner product sign. I have to check that, but only after I return from holidays.--Julius (talk) 22:37, 26 December 2021 (UTC)


 * I would very strongly prefer that the notation remain the same as the source work presents it. If the change from $\det g$ to $g$ is indeed just a notational difference, then we need to set up an "Also presented as" section and explain the meaning and reasons for the differences.


 * In all cases, as you say, the underlying objects need to be carefully and fully defined, in order that, for a start, the notation $\struct {M, g}$ is completely understood. As it stands, the page Definition:Riemannian Manifold may be improved by including the notation and its meaning.


 * Perhaps in the proof itself we implement a "recall" clause for the $\struct {M, g}$, in order to clarify the thinking of the reader and not to demand a prior knowledge of what all this stuff means. --prime mover (talk) 23:19, 26 December 2021 (UTC)


 * I think we simply need to add the determinant of a metric tensor as the third option to Definition:Determinant, next to the determinant of a matrix and a linear operator. And, indeed, there is no excuse to exclude $\struct {M, g}$ from the page that defines this notion. All these standard abreviations should reside in definition pages.--Julius (talk) 18:37, 27 December 2021 (UTC)