Constructions of harmonic polynomial maps between spheres

Hillel Gauchman; Gabor Toth

doi:10.1007/BF01263652

Constructions of harmonic polynomial maps between spheres

Hillel Gauchman, Gabor Toth

Rutgers Camden, Mathematics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

The complexity of λ_q-eigenmaps, i.e. homogeneous degree q harmonic polynomial maps f:S^m →Sⁿ, increases fast with the degree q and the source dimension m. 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.

Original language	English (US)
Pages (from-to)	57-79
Number of pages	23
Journal	Geometriae Dedicata
Volume	50
Issue number	1
DOIs	https://doi.org/10.1007/BF01263652
State	Published - Mar 1994

All Science Journal Classification (ASJC) codes

Geometry and Topology

Keywords

Mathematics Subject Classification (1991): 58E20

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10.1007/BF01263652

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abstract = "The complexity of λq-eigenmaps, i.e. homogeneous degree q harmonic polynomial maps f:Sm →Sn, increases fast with the degree q and the source dimension m. 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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AB - The complexity of λq-eigenmaps, i.e. homogeneous degree q harmonic polynomial maps f:Sm →Sn, increases fast with the degree q and the source dimension m. 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.

KW - Mathematics Subject Classification (1991): 58E20

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Constructions of harmonic polynomial maps between spheres

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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