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T^{a}_{bc}= [itex]\Gamma[/itex]^{a}_{bc}- [itex]\Gamma[/itex]^{a}_{cb}

is a Tensor of rank (1,2)

Attempted solution:

1. Using definition of Covariant Derivative:

D_{b}T^{a}= ∂_{a}T^{a}+[itex]\Gamma[/itex]^{a}_{bc}T^{c}(1)

D_{c}T^{a}= ∂_{c}T^{a}+[itex]\Gamma[/itex]^{a}_{cb}T^{b}(2)

I subtracted (2) from (1) but I couldn't really get a Tensor out of it. I just got lost in the mess.

Is this is the right way to start it?

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# Antisymmetric connection (Torsion Tensor)

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