Examples of Non-Conformal Submersions from Spheres with Umbilical Fibers

Abstract

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