A Space of Harmonic Maps from the Sphere into the Complex Projective Space

http://dx.doi.org/10.4153/CJM-2012-052-6
21 pages

  Published:2012-12-29
 

Guest-Ohnita and Crawford have shown the path-connectedness of the space of harmonic maps from $S^2$ to $\mathbf{C} P^n$ of a fixed degree and energy.It is well-known that the $\partial$ transform is defined on this space. In this paper,we will show that the space is decomposed into mutually disjoint connected subspaces on which $\partial$ is homeomorphic.