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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.