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2016 Riemannian foliations of spheres
Alexander Lytchak, Burkhard Wilking
Geom. Topol. 20(3): 1257-1274 (2016). 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.

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Alexander Lytchak. Burkhard Wilking. "Riemannian foliations of spheres." Geom. Topol. 20 (3) 1257 - 1274, 2016. https://doi.org/10.2140/gt.2016.20.1257

Information

Received: 12 December 2013; Revised: 27 April 2015; Accepted: 15 July 2015; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 1361.53022
MathSciNet: MR3523057
Digital Object Identifier: 10.2140/gt.2016.20.1257

Subjects:
Primary: 53C12, 57R30

Rights: Copyright © 2016 Mathematical Sciences Publishers

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