On the Construction of p-Harmonic Morphisms and Conformal Actions

Abstract

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 ℝm\{0} to ℝn. 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 : ℝm\{0} → ℝn where m = 2kδ(n − 1).