Jacobi Fields Along Harmonic 2-Spheres in CP2 are Integrable

The paper shows that any Jacobi field along a harmonic map fromthe 2-sphere to the complex projective plane is integrable (thatis, is tangent to a smooth variation through harmonic maps).This provides one of the few known answers to the problem ofintegrability, which was raised in different contexts of geometryand analysis. It implies that the Jacobi fields form the tangentbundle to each component of the manifold of harmonic maps fromS² to CP² thus giving the nullity of any such harmonic map;it also has a bearing on the behaviour of weakly harmonic E-minimizingmaps from a 3-manifold to CP² near a singularity and the structureof the singular set of such maps from any manifold to CP².