Clifford algebras and new singular Riemannian foliations in spheres

TL;DR

This paper introduces a novel method for constructing indecomposable singular Riemannian foliations on spheres using Clifford algebra representations, expanding the class of known non-homogeneous foliations beyond previous isoparametric hypersurfaces.

Contribution

It generalizes the construction of non-homogeneous isoparametric hypersurfaces by employing Clifford algebra representations to produce new singular Riemannian foliations.

Findings

Constructed new indecomposable singular Riemannian foliations on spheres.

Most of these foliations are non-homogeneous.

Extends the class of known non-homogeneous foliations beyond classical isoparametric examples.

Abstract

Using representations of Clifford algebras we construct indecomposable singular Riemannian foliations on round spheres, most of which are non-homogeneous. This generalizes the construction of non-homogeneous isoparametric hypersurfaces due to by Ferus, Karcher and Munzner.