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.
|Original language||English (US)|
|Number of pages||23|
|State||Published - Mar 1994|
All Science Journal Classification (ASJC) codes
- Geometry and Topology
- Mathematics Subject Classification (1991): 58E20