hello, i have met with a problem. please help me. A Lie group,with a left-invariant Riemannian metric, i want to compute the connection compatible with the Riemannian metric. C(ij, k) are the structure constants, g(ij) are the metric, then how to compute the Riemannian connection in terms of g(ij) and C(ij, k)? thanks a lot.