Geometry & Topology

Nonnegatively curved $5$–manifolds with almost maximal symmetry rank

Fernando Galaz-Garcia and Catherine Searle

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Abstract

We show that a closed, simply connected, nonnegatively curved 5–manifold admitting an effective, isometric T2 action is diffeomorphic to one of S5,S3×S2, S3×̃S2 or the Wu manifold SU(3)SO(3).

Article information

Source
Geom. Topol., Volume 18, Number 3 (2014), 1397-1435.

Dates
Received: 5 July 2012
Revised: 8 November 2013
Accepted: 14 December 2013
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513732798

Digital Object Identifier
doi:10.2140/gt.2014.18.1397

Mathematical Reviews number (MathSciNet)
MR3228455

Zentralblatt MATH identifier
1294.53038

Subjects
Primary: 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20]
Secondary: 57S25: Groups acting on specific manifolds 51M25: Length, area and volume [See also 26B15]

Keywords
symmetry rank nonnegative curvature $5$–manifold torus action

Citation

Galaz-Garcia, Fernando; Searle, Catherine. Nonnegatively curved $5$–manifolds with almost maximal symmetry rank. Geom. Topol. 18 (2014), no. 3, 1397--1435. doi:10.2140/gt.2014.18.1397. https://projecteuclid.org/euclid.gt/1513732798


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