On the classification of quadratic harmonic morphisms between Euclidean spaces

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dc.creatorOu, Ye-lin
dc.creatorWood, J. C.
dc.date1995-11-03
dc.date.accessioned2026-07-07T09:12:37Z
dc.date.available2026-07-07T09:12:37Z
dc.descriptionWe 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 R}^{4}\longrightarrow {\Bbb R}^{3} $, 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 ${\Bbb S}^{3} \longrightarrow {\Bbb S}^{2}$.
dc.description13 pages, AMS-Latex
dc.identifierhttps://arxiv.org/abs/dg-ga/9511002
dc.identifierhttp://arxiv.org/abs/dg-ga/9511002
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/152083
dc.subjectDifferential Geometry
dc.titleOn the classification of quadratic harmonic morphisms between Euclidean spaces
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