Bolton, J. and Woodward, L. M. (2006) 'The space of harmonic two-spheres in the unit four-sphere.', Tohoku mathematical journal., 58 (2). pp. 231-236.
A harmonic map of the Riemann sphere into the unit 4-dimensional sphere has area 4 pi d for some positive integer d, and it is well-known that the space of such maps may be given the structure of a complex algebraic variety of dimension 2d+4. When d is less than or equal to 2, the subspace consisting of those maps which are linearly full is empty. We use the twistor fibration from complex projective 3-space to the 4-sphere to show that, if d is equal to 3,4 or 5, this subspace is a complex manifold.
|Keywords:||Harmonic maps, 2-sphere, Twistor fibration.|
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|Publisher Web site:||http://dx.doi.org/10.2748/tmj/1156256402|
|Record Created:||06 Mar 2008|
|Last Modified:||08 Apr 2009 16:30|
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