I know that $\langle U,V \rangle = \langle dR_{x_{t(e)}}U, dR_{x_{t(e)}}V \rangle$ and $\langle U,V \rangle = \langle dL_{x_{t(e)}}U, dL_{x_{t(e)}}V \rangle$ because it is bi-invariant. How do I proceed?
2026-05-06 07:24:18.1778052258
Show that $\langle[U,X],V\rangle = -\langle U,[V,X]\rangle$ for bi-invariant metric in Lie group
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