Volume 20, issue 3 (2016)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
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
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