Right-invariant Riemannian metric
= Right-invariant Riemannian metric
{title2=$R_g^*h=h$}
A <Riemannian metric> on a <Lie group> is right-invariant when every right translation is an <isometry>. It is determined by a positive-definite <inner product> at the identity, extended with a coframe of <right-invariant differential forms>. Its translation-generated <Killing vector fields> are left-invariant, rather than the right-invariant vector fields dual to that coframe.