The Space of Harmonic Maps from the 2-sphere to the Complex Projective Plane

T. Arleigh Crawford

The Space of Harmonic Maps from the 2-sphere to the Complex Projective Plane

dg-ga 2008-02-03 v1 Differential Geometry

Authors: T. Arleigh Crawford

Abstract

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.

Keywords

harmonic maps S^2 complex projective plane path connected complex manifolds

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@article{arxiv.dg-ga/9512004,
  title  = {The Space of Harmonic Maps from the 2-sphere to the Complex Projective Plane},
  author = {T. Arleigh Crawford},
  journal= {arXiv preprint arXiv:dg-ga/9512004},
  year   = {2008}
}

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Plain TeX, 11 pages, no figures

The Space of Harmonic Maps from the 2-sphere to the Complex Projective Plane

Abstract

Keywords

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