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# The space of harmonic maps from the $2$-sphere to the complex projective plane

Published:1997-09-01
Printed: Sep 1997
• T. Arleigh Crawford
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## Abstract

In this paper 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.
 MSC Classifications: 58E20 - Harmonic maps [See also 53C43], etc. 58D27 - Moduli problems for differential geometric structures