Riemannian foliations of spheres

Abstract

We show that a Riemannian foliation on a topological $n$–sphere has leaf dimension $1$ or $3$ unless $n=15$ and the Riemannian foliation is given by the fibers of a Riemannian submersion to an $8$–dimensional sphere. This allows us to classify Riemannian foliations on round spheres up to metric congruence.