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.(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# Zero connection => Zero torsion tensor ?

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