Isometry group
= Isometry group
{title2=$\operatorname{Isom}(M,h)$}
The <isometry group> of a <metric space> consists of its bijective <isometries>, with composition as the group operation. For a <Riemannian metric>, these are the <diffeomorphisms> preserving the <metric tensor>. Right translations of a <right-invariant Riemannian metric> supply a faithful subgroup isomorphic to the underlying <Lie group>.