List of contributions

Harmonic maps between Riemannian manifolds are maps which extremize a certain natural energy functional; they appear in particle physics as nonlinear sigma models. Their infinitesimal deformations are called Jacobi fields. It is important to know whether the Jacobi fields along the harmonic maps between given Riemannian manifolds are integrable, i.e., arise from genuine variations through harmonic maps. If they do, then the space of harmonic maps is a smooth manifold with tangent space given by the Jacobi fields; in the case of harmonic maps from the 2sphere we also gain some information on the structure of the singular set of weakly harmonic maps from an arbitrary manifold. We shall outline what is known about Jacobi fields and their integrability concentrating on the case of harmonic maps from the 2-sphere to the 4-sphere.