On the Construction of p-Harmonic Morphisms and Conformal Actions

Xiao Huan Mo; Li Bing Huang; Yuan Zheng Zhang
August 2007
Acta Mathematica Sinica;Aug2007, Vol. 23 Issue 8, p1475
Academic Journal
We produce p-harmonic morphisms by conformal foliations and Clifford systems. First, we give a useful criterion for a foliation on an m-dimensional Riemannian manifold locally generated by conformal fields to produce p-harmonic morphisms. By using this criterion we manufacture conformal foliations, with codimension not equal to p, which are locally the fibres of p-harmonic morphisms. Then we give a new approach for the construction of p-harmonic morphisms from ℝ m \{0} to ℝ n . By the well-known representation of Clifford algebras, we find an abundance of the new $$ \frac{2} {3}{\left( {m + 1} \right)} $$ -harmonic morphism ϕ : ℝ m \{0} → ℝ n where m = 2 kδ( n − 1).


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