Riemannian connection of a Lie group

[marton]

This is problem in the book of Riemmannian manifolds an introduction to curvature, pp. 89. The author is John M. Lee.

Suppose G is a Lie group with Lie algebra g, and let (X1, ..., Xn) be any basis of g. Define the structure constants C(ij, k) by

[Xi, Xj] = C(ij, k)Xk

For an arbitrary left-invariant metric g on G, computet the Chrisffel symbols of the Riemnnian connections in terms of g(ij) and C(ij, k)

Thanks a lot.