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

  title={The Space of Harmonic Maps from the 2-sphere to the Complex Projective Plane},
  author={Tim Crawford},
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≥2. We show that the components of maps to CP 2 are complex manifolds. Harmonic maps from the Riemann sphere to complex projective space are critical points of the energy functional defined on the space of… CONTINUE READING


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