Tohoku Mathematical Journal

The space of harmonic two-spheres in the unit four-sphere

John Bolton and Lyndon M. Woodward

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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 $d$ 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.

Article information

Source
Tohoku Math. J. (2), Volume 58, Number 2 (2006), 231-236.

Dates
First available in Project Euclid: 22 August 2006

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1156256402

Digital Object Identifier
doi:10.2748/tmj/1156256402

Mathematical Reviews number (MathSciNet)
MR2248431

Zentralblatt MATH identifier
1106.58006

Subjects
Primary: 58D10: Spaces of imbeddings and immersions
Secondary: 53C43: Differential geometric aspects of harmonic maps [See also 58E20]

Keywords
Harmonic maps 2-sphere twistor fibration

Citation

Bolton, John; Woodward, Lyndon M. The space of harmonic two-spheres in the unit four-sphere. Tohoku Math. J. (2) 58 (2006), no. 2, 231--236. doi:10.2748/tmj/1156256402. https://projecteuclid.org/euclid.tmj/1156256402


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