Jacobi fields along harmonic 2-spheres in 3- and 4-spheres are not all integrable (Q843027)

This is a very interesting paper and gives the striking result that there are non-full harmonic maps \(S^2\to S^3\), \(S^4\) with Jacobi fields that are non-integrable in the sense that they do not arise (at tangents) from smooth variations. Since the space of harmonic maps \(S^2\to S^3\) (of a given degree) is a smooth manifold, this result defies the rather simplified view of Jacobi fields as being tangent vectors at the respective harmonic maps, at least in the smooth case.