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I seem to be having difficulty proving something.

I hope you can help me.

I will write del_X(Y) when I refer to the levi-chivita connection (used on Y in the direction of X).

Let G be a lie group, with a bi-invariant metric , g , on G.

I want to prove that del_X(Y) = 0.5 [X,Y] (Lie brackets) , whenever X,Y are left-invariant vector fields on G.

Thanks in advance.

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# Lie group geometry

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