The geometry of conformal foliations and p-harmonic morphisms
Published online by Cambridge University Press: 27 August 2003
By defining new Bryant-type vector fields for foliations on a Riemannian manifold we find necessary and sufficient conditions that a foliation produces $p$-harmonic morphisms. Two applications are given. First, we characterize one-parameter conformal actions using $p$-harmonic morphisms. Then we classify $p$-harmonic morphisms on a constant curvature space with one-dimensional fibres by studying bi-minimal distributions. We also give a description of all conformal foliations which have minimal fibres on a Riemannian manifold in terms of $p$-harmonic morphisms.
- Research Article
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 135 , Issue 2 , September 2003 , pp. 321 - 334
- 2003 Cambridge Philosophical Society