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The space of harmonic maps from the $2$-sphere to the complex projective plane |
Canad. Math. Bull. 40(1997), 285-295
Published:1997-09-01
Printed: Sep 1997
Printed: Sep 1997
- T. Arleigh Crawford
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 |