Volume 20, issue 3 (2016)

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Riemannian foliations of spheres

Alexander Lytchak and Burkhard Wilking

Geometry & Topology 20 (2016) 1257–1274
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.

Keywords
Riemannian foliations, generalized Seifert fibrations, orbifolds
Mathematical Subject Classification 2010
Primary: 53C12, 57R30