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Demonstratio Mathematica

Editor-in-Chief: Vetro, Calogero

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Volume 47, Issue 3


Examples of Non-Conformal Submersions from Spheres with Umbilical Fibers

Tomasz Zawadzki
Published Online: 2014-09-02 | DOI: https://doi.org/10.2478/dema-2014-0059


We directly prove that the foliation of the sphere S2n+1, the leaves of which are intersections of all complex linear 2-dimensional subspaces of ℂn+1 translated by a constant vector p, defines a submersion that is horizontally conformal if and only if p=0. We generalise this result to the cases of S4n+3 and S15 with foliations constructed using quaternionic and octonionic structure (resp.) in an analogous way

Keywords: and phrases: foliation; conformal submersion; spheres


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About the article

Received: 2013-02-18

Revised: 2013-04-16

Published Online: 2014-09-02

Published in Print: 2014-07-01

Citation Information: Demonstratio Mathematica, Volume 47, Issue 3, Pages 738–747, ISSN (Online) 2391-4661, ISSN (Print) 0420-1213, DOI: https://doi.org/10.2478/dema-2014-0059.

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© by Tomasz Zawadzki. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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