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

Published:2012-12-29
Printed: Aug 2013
• Hiroko Kawabe,
Toin University of Yokohama, 1614,Kurogane-Cho,Aoba-Ku,Yokohama-Shi 225-8502, Japan
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## Abstract

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.
 Keywords: harmonic maps, harmonic sequences, gluing