Clifford algebras and new singular Riemannian foliations in spheres

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.

21 pages. Construction of foliations in the Cayley plane added. Proofs simplified and presentation improved, according to referee's suggestions. To appear in Geom. Funct. Anal

References in corpus (2)

• Isometric actions on spheres with an orbifold quotient
• Riemannian foliations of spheres

Cited by in corpus (2)

• Focal Radius, Rigidity, and Lower Curvature Bounds
• Mean curvature flow of singular Riemannian foliations