Hello everyone,
I have what I think should be some very basic questions, but I honestly can't figure them out:
Consider that a metric and a chart are defined in a given manifold, and then you define two 2-tensors A and B. In the attached notebook I use the Schwarzschild metric and two random 2-vectors as example. The questions are:
1.- Why does the contraction A[-a,-i] B[i,b] give something of the form CTensor[...][b,-a] instead of
CTensor[...][-a,b]? (like in [15] in the notebook)
2.- Why doesn't HeadOfTensor[
A[-a,-i] B[i,b]
,{-a,b}][b,-a] give the same result as before? (see [16] in the notebook)
3.- Why do I need to write
HeadOfTensor[
A[-a,-i] B[i,b]
,{-a,b}][-a,b] to get what I expected to obtain from
A[-a,-i] B[i,b]? (see [17])
Something similar happens with more complicated contractions of tensors with more indices and I don't know what is going on.
Thank you very much in advance for your help.
Cheers,
Salva