Constructions of harmonic polynomial maps between spheres |
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Authors: | Hillel Gauchman Gabor Toth |
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Institution: | (1) University of Illinois, 61801 Urbana-Chaimpaign, IL, USA;(2) Eastern Illinois University, 61920 Charleston, IL, USA;(3) Rutgers University, 08102 Camden, NJ, USA |
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Abstract: | The complexity of
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 2-eigenmaps. |
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Keywords: | 58E20 |
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