Skyrmions, instantons, mass and curvature

We show that skyrmions with massless pions in hyperbolic space provide a good approximation to skyrmions with massive pions in Euclidean space, for a particular relationship between the pion mass and the curvature of hyperbolic space. Using this result we describe how a skyrmion with massive pions in Euclidean space can be approximated by the holonomy along circles of a Yang-Mills instanton. This is a generalization of the approximation of skyrmions by the holonomy along lines of an instanton, which is only applicable to massless pions.