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On the geometry of the Gauss map of conformal foliations by lines

Published online by Cambridge University Press:  15 January 2004

JEAN-MARIE BUREL  and
SIGMUNDUR GUDMUNDSSON
JEAN-MARIE BUREL
Affiliation:
Mathematics, Faculty of Science, Lund University, Box 118, S-221 00 Lund, Sweden. e-mail: Jean-Marie.Burel@math.lu.se
SIGMUNDUR GUDMUNDSSON
Affiliation:
Mathematics, Faculty of Science, Lund University, Box 118, S-221 00 Lund, Sweden. e-mail: Sigmundur.Gudmundsson@math.lu.se
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Abstract

Let ${\cal F}$ be an oriented conformal foliation of connected, totally geodesic and 1-dimensional leaves in $\mathbb{R}^{n+1}$. We prove that if $n\geq 3$ then the Gauss map $\phi{:}\,\,U\,{\to}\,S^n$ of ${\cal F}$ is a non-constant $n$-harmonic morphism if and only if it is a radial projection.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 136 , Issue 1 , January 2004 , pp. 247 - 255
Copyright
2004 Cambridge Philosophical Society

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