  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.

Differential Geometry;Differential Geometry