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Quadratic harmonic morphisms and O-systems

Ye-Lin Ou — 1997

Annales de l'institut Fourier

We introduce O-systems (Definition 3.1) of orthogonal transformations of m , and establish correspondences both between equivalence classes of Clifford systems and those of O-systems, and between O-systems and orthogonal multiplications of the form μ : n × m 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...

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