Quadratic harmonic morphisms and O-systems

Ye-Lin Ou

Annales de l'institut Fourier (1997)

  • Volume: 47, Issue: 2, page 687-713
  • ISSN: 0373-0956

Abstract

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We introduce O-systems (Definition 3.1) of orthogonal transformations of ℝ m , and establish ℝ correspondences both between equivalence classes of Clifford systems and those of O-systems, and between O-systems and orthogonal multiplications of the form μ : ℝ n × ℝ m → ℝ m , which allow us to solve the existence problems both for O -systems and for umbilical quadratic harmonic morphisms simultaneously. The existence problem for general quadratic harmonic morphisms is then solved by the Splitting Lemma. We also study properties possessed by all quadratic harmonic morphisms for fixed pairs of domain and range spaces.

How to cite

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Ou, Ye-Lin. "Quadratic harmonic morphisms and O-systems." Annales de l'institut Fourier 47.2 (1997): 687-713. <http://eudml.org/doc/75242>.

@article{Ou1997,
abstract = {We introduce O-systems (Definition 3.1) of orthogonal transformations of $\{\Bbb R\}^m$, and establish $\{\Bbb R\}$ correspondences both between equivalence classes of Clifford systems and those of O-systems, and between O-systems and orthogonal multiplications of the form $\mu : \{\Bbb R\}^n\times \{\Bbb R\}^m\rightarrow \{\Bbb R\}^m$, which allow us to solve the existence problems both for $O$-systems and for umbilical quadratic harmonic morphisms simultaneously. The existence problem for general quadratic harmonic morphisms is then solved by the Splitting Lemma. We also study properties possessed by all quadratic harmonic morphisms for fixed pairs of domain and range spaces.},
author = {Ou, Ye-Lin},
journal = {Annales de l'institut Fourier},
keywords = {harmonic applications; quadratic harmonic morphisms; -systems; Clifford systems},
language = {eng},
number = {2},
pages = {687-713},
publisher = {Association des Annales de l'Institut Fourier},
title = {Quadratic harmonic morphisms and O-systems},
url = {http://eudml.org/doc/75242},
volume = {47},
year = {1997},
}

TY - JOUR
AU - Ou, Ye-Lin
TI - Quadratic harmonic morphisms and O-systems
JO - Annales de l'institut Fourier
PY - 1997
PB - Association des Annales de l'Institut Fourier
VL - 47
IS - 2
SP - 687
EP - 713
AB - We introduce O-systems (Definition 3.1) of orthogonal transformations of ${\Bbb R}^m$, and establish ${\Bbb R}$ correspondences both between equivalence classes of Clifford systems and those of O-systems, and between O-systems and orthogonal multiplications of the form $\mu : {\Bbb R}^n\times {\Bbb R}^m\rightarrow {\Bbb R}^m$, which allow us to solve the existence problems both for $O$-systems and for umbilical quadratic harmonic morphisms simultaneously. The existence problem for general quadratic harmonic morphisms is then solved by the Splitting Lemma. We also study properties possessed by all quadratic harmonic morphisms for fixed pairs of domain and range spaces.
LA - eng
KW - harmonic applications; quadratic harmonic morphisms; -systems; Clifford systems
UR - http://eudml.org/doc/75242
ER -

References

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