Dr John Bolton john.bolton@durham.ac.uk
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The space of harmonic two-spheres in the unit four-sphere
Bolton, John; Woodward, L.M.
Authors
L.M. Woodward
Abstract
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.
Citation
Bolton, J., & Woodward, L. (2006). The space of harmonic two-spheres in the unit four-sphere. Tohoku mathematical journal, 58(2), 231-236. https://doi.org/10.2748/tmj/1156256402
Journal Article Type | Article |
---|---|
Publication Date | 2006-03 |
Deposit Date | Mar 6, 2008 |
Journal | Tohoku mathematical journal |
Print ISSN | 0040-8735 |
Publisher | Mathematical Institute of Tohoku University |
Peer Reviewed | Peer Reviewed |
Volume | 58 |
Issue | 2 |
Pages | 231-236 |
DOI | https://doi.org/10.2748/tmj/1156256402 |
Keywords | Harmonic maps, 2-sphere, Twistor fibration. |
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