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).
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Loubeau, E.: On p-harmonic morphisms. Differential Geometry and its Applications, 12, 219–229 (2000)
Mo, X.: The geometry of conformal foliations and p-harmonic morphisms. Math. Proc. Cambridge Phios. Soc., 135, 321–334 (2003)
Baird, P., Gudmundsson, S.: p-harmonic maps and minimal submanifolds. Math. Ann., 294, 611–624 (1992)
Tondeur, Th.: Geometry of foliations, Monographs in Mathematics 90, Birkhäuser-Verlag, Basel, 1997
Pantilie, R.: Conformal actions and harmonic morphisms. Math. Proc. Cambridge Phios. Soc., 129, 527–547 (2000)
Pantilie, R.: Harmonic morphisms with one-dimensional fibres. Internat. J. Math., 10, 457–501 (1999)
Pantilie, R.: Isometric actions and harmonic morphisms. Michigan Math. J., 47, 453–467 (2000)
Pantilie, R.: Harmonic morphisms with 1-dimensional fibres on 4-dimensional Einsten manifolds. Comm. Anal. Geom., 10, 779–814 (2002)
Wood, J. C.: Harmonic morphisms, foliations and Gauss maps. Complex Differential Geometry and Nonlinear Differential Equations, 145-183, Contemp. Math., 49 (Amer. Math. Soc., Providence, R.I., 1986)
Husemoller, D.: Fibre bundles, 3rd edn., Graduate Texts in Mathematics, Vol. 20, Springer, New York, (1st edn. McGraw Hill, New York, 1966)
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This work is supported by the National Natural Science Foundation of China (10471001)
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Mo, X.H., Huang, L.B. & Zhang, Y.Z. On the Construction of p-Harmonic Morphisms and Conformal Actions. Acta Math Sinica 23, 1475–1484 (2007). https://doi.org/10.1007/s10114-005-0896-7
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DOI: https://doi.org/10.1007/s10114-005-0896-7