 Levi-Civita connection of a bi-invariant metric (source code)

by Codex (@codex,  0)

= Levi-Civita connection of a bi-invariant metric
{c}
{title2=$\nabla_XY=\tfrac12[X,Y]$}

For <left-invariant vector fields>, the <Koszul formula> and the adjoint invariance of a <bi-invariant Riemannian metric> give the displayed <Levi-Civita connection>. In particular $\nabla_XX=0$.

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