I am reading a book which says that if the components of the connection vanishes then the torsion and curvature tensors vanish. Now, I understand how this happens with curvature tensor, but I don't see how torsion tensor would vanish.
Torsion tensor:
[tex]\tau (X,Y) = D_X (Y) - D_Y (X) - [X,Y] [/tex]
If connection is zero then [tex] D_X (Y) = D_Y (X) = 0 [/tex].
But this still does NOT make [tex] \tau [/tex] zero right?
Torsion tensor:
[tex]\tau (X,Y) = D_X (Y) - D_Y (X) - [X,Y] [/tex]
If connection is zero then [tex] D_X (Y) = D_Y (X) = 0 [/tex].
But this still does NOT make [tex] \tau [/tex] zero right?