The space of harmonic two-spheres in the unit four-sphere
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.
scientific article; zbMATH DE number 5076983
scientific article