Year: 2025
Type: article
Abstract: The eigenfamilies of Gudmundsson and Sakovich (Ann Global Anal Geom 33(4):343–356, 2008) can be used to generate harmonic morphisms, proper r-harmonic maps, and minimal co-dimension 2 submanifolds. This article begins by characterising the globally defined eigenfamilies of the sphere $$S^m$$ S m ; they correspond to orthogonal families of homogeneous polynomial harmonic morphisms from $$\mathbb {R}^{m+1}$$ R m + 1 to $$\mathbb {C}$$ C , all of the same degree. We investigate and construct such families, paying special attention to those that are not congruent to families of holomorphic polynomials. Strong restrictions for families of such polynomials are found in low dimensions, and the pairs of degree 2 maps that induce an eigenfamily are classified.
Source: Mathematische Zeitschrift
Author: Oskar Riedler
Institution: University of Potsdam
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
OpenAlex ID: W4414196561