Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-28T13:48:46.881Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
SIGMUNDUR GUDMUNDSSON
Affiliation:
Mathematics, Faculty of Science, Lund University, Box 118, S-221 00 Lund, Sweden. e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)