The Space of Harmonic Maps from the 2-sphere to the Complex Projective Plane

We study the topology of the space of harmonic maps from $S^2$ to \CP 2$. We prove that the subspaces consisting of maps of a fixed degree and energy are path connected. By a result of Guest and Ohnita it follows that the same is true for the space of harmonic maps to$\CP n$for$n\geq 2$. We show that the components of maps to$\CP 2$ are complex manifolds.Comment: Plain TeX, 11 pages, no figure