Does Metric Signature Affect Torsion Definition?

[binbagsss]

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.

 

[robphy]

What are those sources?
What are their definitions of Riemann and Ricci?