The space of harmonic two-spheres in the unit four-sphere
type: Item
instance of: scholarly article
title: The space of harmonic two-spheres in the unit four-sphere
zbMATH Open document ID: 1106.58006
author: John Bolton
author: Lyndon M. Woodward
published in: Tôhoku Mathematical Journal. Second Series
publication date: 2006-12-04T00:00:00Z
full work available at URL: tohokumathjen.html
review text: It is known that a harmonic map of the Riemann sphere into the 4-dimensional unit sphere has area \(4\pi d\) for some positive integer \(d\), and that the space of such maps may be given a structure of a complex algebraic variety of dimension \(2d+4\). Further, it is a known fact that for \(d\) less or equal to \(2\), the subspace which consists of those maps which are linearly full, is empty. Using the twistor fibration from complex projective 3-space to the 4-sphere, the authors prove that, for \(d\in\{3,4,5\}\), this subspace is a complex manifold.
reviewed by: Vladimir Balan
Mathematics Subject Classification ID: 58D10
Mathematics Subject Classification ID: 53C43
Mathematics Subject Classification ID: 58E20
zbMATH DE Number: 5076983
zbMATH Keywords: harmonic maps
zbMATH Keywords: 2-sphere
zbMATH Keywords: four-sphere
zbMATH Keywords: twistor fibration
MaRDI profile type: Publication
OpenAlex ID: W2015603408
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DOI: 10.2748/TMJ/1156256402
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description: scientific article; zbMATH DE number 5076983