On the classification of quadratic harmonic morphisms between Euclidean spaces

1995/11/03 by Ye‐Lin Ou, Ye-lin Ou, J. C. Wood +3
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Analysis Techniques #Differential Geometry (math.DG) #FOS: Mathematics #dg-ga #math.DG

paper · pdf · doi:10.48550/arxiv.dg-ga/9511002

13 pages, AMS-Latex

arxiv created 1995/11/03 · openalex publication_date 1995/11/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a classification of quadratic harmonic morphisms between Euclidean spaces (Theorem 2.4) after proving a Rank Lemma. We also find a correspondence between umbilical (Definition 2.7) quadratic harmonic morphisms and Clifford systems. In the case \Bbb R⁴\longrightarrow \Bbb R³ , we determine all quadratic harmonic morphisms and show that, up to a constant factor, they are all bi-equivalent (Definition 3.2) to the well-known Hopf construction map and induce harmonic morphisms bi-equivalent to the Hopf fibration \Bbb S³ \longrightarrow \Bbb S².

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