- #1
member 11137
I am really confused and the question can appear to be trivial or stupid:
Is the Ricci tensor symmetric or anti-symmetric in a torsion-free affine connection?
I am full of troubles since two different references gives two different answers (sorry no one is in english language but one of them is Lichnerowicz and the latter indicates an antisymmetric Ricci tensor whilst the other -based on the tensor calculus and on the expression of the curvature tensor Rabcd- tells me that Ricci is symmetric) !
Thanks for some feed-back and sorry if it is not the good place to post.
Is the Ricci tensor symmetric or anti-symmetric in a torsion-free affine connection?
I am full of troubles since two different references gives two different answers (sorry no one is in english language but one of them is Lichnerowicz and the latter indicates an antisymmetric Ricci tensor whilst the other -based on the tensor calculus and on the expression of the curvature tensor Rabcd- tells me that Ricci is symmetric) !
Thanks for some feed-back and sorry if it is not the good place to post.