Abstract
The spaces of harmonic maps of the projective plane to the four-dimensional sphere are investigated in this paper by means of twistor lifts. It is shown that such spaces are empty in case of even harmonic degree. In case of harmonic degree less than 6 it was shown that such spaces are path-connected and an explicit parameterization of the canonical representatives was found. In addition, the last section provides comparisons with the known results for harmonic maps of the two-dimensional sphere to the four-dimensional sphere of harmonic degree less than 6.
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Author is thankful to Alexei V. Penskoi for attaching the author’s attention to this problem, helpful remarks and useful conversations.
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Gabdurakhmanov, R. Spaces of harmonic maps of the projective plane to the four-dimensional sphere. J. Geom. 111, 40 (2020). https://doi.org/10.1007/s00022-020-00550-7
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DOI: https://doi.org/10.1007/s00022-020-00550-7