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## Main Question or Discussion Point

Given an antisymmetric tensor

[itex]T^{ab}=-T^{ab}[/itex]

show that

[itex]T_{ab;c} + T_{ca;b} + T_{bc;a} = 0[/itex]

If I explicitly write out the covariant derivative, all terms with Christoffel symbols cancel pair-wise, and I'm left to demonstrate that

[itex]T_{ab,c} + T_{ca,b} + T_{bc,a} = 0[/itex]

and this I have no idea how to do. Could anybody put me on the right track please?

[itex]T^{ab}=-T^{ab}[/itex]

show that

[itex]T_{ab;c} + T_{ca;b} + T_{bc;a} = 0[/itex]

If I explicitly write out the covariant derivative, all terms with Christoffel symbols cancel pair-wise, and I'm left to demonstrate that

[itex]T_{ab,c} + T_{ca,b} + T_{bc,a} = 0[/itex]

and this I have no idea how to do. Could anybody put me on the right track please?