First of all, this question is about tensor analysis and not scalar product.
I was reading "Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers" by Nguyen-Schäfer, Hung, Schmidt, Jan-Philip ISBN 978-3-662-48495-1.
In this book, it is stated that a symbol is used in a tensor index:
Note that in Eq. (2.70),, the dot after the lower index indicates the position of the basis of the upper index locating after the tensor T
And the equation (2.70) has the tensor $T_ { i. }^ { i }$ in it for example.
- Does this "dot" have a better name?
- Is it possible to have a more precise definition?
- Is it possible to have an unambigous example of the . symbol in action?
This is a typographical helper and not that usual in tensor notations. Usually you can see in the spacing of the indices the position, but with italics/cursive it might be ambiguous. $T{}_i{}^{jk}{}_m{}^n$ vs. roman $\mathrm{T{}_i{}^{jk}{}_m{}^n}$. It might also help to have a denser source for the text and take less space in the printed text, $T^{.jk.n}_{i..m}$