Geometry of skyrmions

A Skyrmion may be regarded as a topologically non-trivial map from one Riemannian manifold to another, minimizing a particular energy functional. We discuss the geometrical interpretation of this energy functional and give examples of Skyrmions on various manifolds. We show how the existence of conformal transformations can cause a Skyrmion on a 3-sphere to become unstable, and how this may be related to chiral symmetry breaking. (orig.)