Remarks on the minimalities of two-bridge knots in the ribbon concordance poset

Ribbon concordance, which was introduced by Gordon, has given us a new perspective in knot concordance theory. Recently, Agol proved that ribbon concordance forms a partial order. In this note, we focus on the partially ordered set given by Gordon and Agol. In particular, we prove that a twobridge knot is minimal in the poset if and only if it is not smoothly concordant to any torus knot or it is a torus knot.