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The geometry of conformal foliations and p-harmonic morphisms

Published online by Cambridge University Press:  27 August 2003

LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, P.R. China. e-mail:


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
2003 Cambridge Philosophical Society

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This work is supported by the National Natural Science Foundation of China (10171002).