Quadratic harmonic morphisms and O-systems
| dc.creator | Ou, Ye-lin | |
| dc.date | 1995-11-03 | |
| dc.date.accessioned | 2026-07-07T09:12:37Z | |
| dc.date.available | 2026-07-07T09:12:37Z | |
| dc.description | We introduce O-systems (Definition \ref{DO}) of orthogonal transformations of ${\Bbb R}^{m}$, and establish $1-1$ correspondences both between equivalence classes of Clifford systems and that of O-systems, and between O-systems and orthogonal multiplications of the form $μ:{\Bbb R}^{n} \times {\Bbb R}^{m} \longrightarrow {\Bbb R}^{m} $, which allow us to solve the existence problems both for O-systems and for umbilical quadratic harmonic morphisms (Theorems \ref{ES} and \ref{EU}) simultaneously. The existence problem for general quadratic harmonic morphisms is then solved (Theorem \ref{EG}) by the Splitting Lemma (Lemma \ref{Split}). We also study properties (see, e.g., Theorems \ref{single} and \ref{TL}) possessed by all quadratic harmonic morphisms for fixed pairs of domain and range spaces (\S5). | |
| dc.description | 30 pages, AMS-Latex | |
| dc.identifier | https://arxiv.org/abs/dg-ga/9511001 | |
| dc.identifier | http://arxiv.org/abs/dg-ga/9511001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152082 | |
| dc.subject | Differential Geometry | |
| dc.title | Quadratic harmonic morphisms and O-systems | |
| dc.type | text |