Right‐invariant metrics on the Lie group SU(3) and the Gell‐Mann–Okubo formula

The classification of right-invariant Riemannian metrics (and Riemannian structures) on SU( 3) is studied and a parametrization for all of them will be given. It will be indicated how to discuss flavor symmetry breaking in hadronic physics using this language long with a geometrical interpretation for the Gell-Mann-Okubo formula.