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

2016/10/17 by Ravil Gabdurakhmanov, Gabdurakhmanov, Ravil
Mathematics · Physics and Astronomy · #53C28 #53C43 #58E20 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematics and Applications #math.DG #msc:53C28 #msc:53C43 #msc:58E20

paper · pdf · doi:10.48550/arxiv.1610.05277

22 pages

openalex publication_date 2016/10/17 · arxiv created 2019/11/07 · arxiv updated 2019/11/11 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

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 summarizes 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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