Abstract
The complexity of λ q -eigenmaps, i.e. homogeneous degreeq harmonic polynomial mapsf:S m →S n, increases fast with the degreeq and the source dimensionm. Here we introduce a variety of methods of manufacturing new eigenmaps out of old ones. They include degree and source dimension raising operators. As a byproduct, we get estimates on the possible range dimensions of full eigenmaps and obtain a geometric insight of the harmonic product of λ2-eigenmaps.
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Gauchman, H., Toth, G. Constructions of harmonic polynomial maps between spheres. Geom Dedicata 50, 57–79 (1994). https://doi.org/10.1007/BF01263652
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DOI: https://doi.org/10.1007/BF01263652