Quit[]

Quiet@Block[{Print},
<<xAct`xTras`]

DefManifold[MECT,4,IndexRange[a,j]]

DefMetric[-1,metric[-a,-b],CD,PrintAs->"g",CurvatureRelations->True,Torsion->True]

TorsionCD[a,-b,-c]

metric[b,c]*TorsionCD[a,-b,-c]//ContractMetric//ToCanonical

(*I can under stand the following output regarding the antisymmetric property of the torsion with respect to its 3nd and 3rd indices: (((δT)^efg)/((δT)^abc))=(1/2)(δ/((δT)^abc))((T^efg)-(T^egf))*)

VarD[TorsionCD[a,b,c],CD][TorsionCD[e,f,g]]