Staff

Publication details for Dr John Bolton

Bolton, John. & Woodward, L.M. (2006). The space of harmonic two-spheres in the unit four-sphere. Tohoku Mathematical Journal 58(2): 231-236.

• Publication type: Journal papers: academic
• ISSN/ISBN: 0040-8735
• DOI: 10.2748/tmj/1156256402
• Keywords: Harmonic maps; 2-sphere; twistor fibration
• View online: Online version
• Durham research online: DRO record

Author(s) from Durham

• Dr John Bolton

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.