Low dimensional Singular Riemannian Foliations in spheres

Abstract

Singular Riemannian Foliations are particular types of foliations on Riemannian manifolds, in which leaves locally stay at a constant distance from each other. Singular Riemannian Foliations in round spheres play a special role, since they provide "infinitesimal information" about general Singular Riemannian Foliations. In this paper we show that Singular Riemannian Foliations in spheres, of dimension at most 3, are orbits of an isometric group action.

44 pages

References in corpus (5)

• Isoparametric and Dupin Hypersurfaces
• Proofs of Conjectures about singular riemannian foliations
• On smoothness of isometries between orbit spaces
• Isometries between leaf spaces
• Taut Submanifolds and Foliations

Cited by in corpus (6)

• Isometric actions on spheres with an orbifold quotient
• Focal Radius, Rigidity, and Lower Curvature Bounds
• Singular Riemannian foliations and applications to positive and nonnegative curvature
• Mean curvature flow of singular Riemannian foliations
• Problems related to isoparametric theory
• Leaf Space Isometries of Singular Riemannian Foliations and Their Spectral Properties