Does definition of torsion depend upon the metric signature?

I'm looking at 2 sources.



One has it defined as ##T^{c}_{ab}=-\Gamma^{c}_{ab}+\Gamma^{c}_{ba}##

And the other has ##T^{c}_{ab}=\Gamma^{c}_{ab}-\Gamma^{c}_{ba}##



##T## the torsion tensor

and

##\Gamma^{c}_{ab}## the connection.



Or is it more that different texts use different conventions?



Thanks.

Does definition of torsion depend upon the metric signature?