We show that a Riemannian foliation on a topological –sphere has leaf dimension or unless and the Riemannian foliation is given by the fibers of a Riemannian submersion to an –dimensional sphere. This allows us to classify Riemannian foliations on round spheres up to metric congruence.
"Riemannian foliations of spheres." Geom. Topol. 20 (3) 1257 - 1274, 2016. https://doi.org/10.2140/gt.2016.20.1257