Does Metric Signature Affect Torsion Definition?

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