Spaces of harmonic maps of the projective plane to the four-dimensional sphere (Q2210785)

The paper investigates the spaces of harmonic maps of the projective plane to the four-dimensional sphere, by means of twistor lifts. It is shown that such spaces are empty in the case of even harmonic degree. In the case of harmonic degree less than 6 it is proved that such spaces are path-connected and an explicit parameterization of the canonical representatives is found. Moreover, comparisons with the known results for harmonic maps of the two-dimensional sphere to the four-dimensional sphere of harmonic degree less than 6 are provided.