John C. Wood (University of Leeds)
j.c.wood@leeds.ac.uk
We show that any Jacobi field along a harmonic map from the 2-sphere to the complex projective plane is integrable (i.e., is tangent to a smooth variation through harmonic maps). This provides one of the few known answers to this problem of integrability, which was raised in different contexts of geometry and analysis. It implies that the Jacobi fields form the tangent bundle to each component of the manifold of harmonic maps from S2 to CP2 thus giving the nullity of any such harmonic map; it also has bearing on the behaviour of weakly harmonic E-minimizing maps from a 3-manifold to CP2 near a singularity and the structure of the singular set of such maps from any manifold to CP2 (joint work with L. Lemaire).