Riemannian foliations of spheres

Lytchak, Alexander; Wilking, Burkhard

doi:10.2140/gt.2016.20.1257

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Riemannian foliations of spheres

Alexander Lytchak and Burkhard Wilking

Geometry & Topology 20 (2016) 1257–1274

DOI: 10.2140/gt.2016.20.1257

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

References

Publication

Received: 12 December 2013

Revised: 27 April 2015

Accepted: 15 July 2015

Published: 4 July 2016

Proposed: John Lott

Seconded: Tobias H Colding, Dmitri Burago

Authors

Alexander Lytchak
Mathematisches Institut Universität zu Köln Weyertal 86-90 D-50931 Köln Germany

Burkhard Wilking
Mathematisches Institut Universität Münster Einsteinstr. 62 D-48147 Münster Germany

Volume 20, issue 3 (2016)