Nonnegatively curved 5–manifolds with almost maximal symmetry rank

Galaz-Garcia, Fernando; Searle, Catherine

doi:10.2140/gt.2014.18.1397

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

Fernando Galaz-Garcia and Catherine Searle

Geometry & Topology 18 (2014) 1397–1435

DOI: 10.2140/gt.2014.18.1397

Abstract

We show that a closed, simply connected, nonnegatively curved $5$ –manifold admitting an effective, isometric $T^{2}$ action is diffeomorphic to one of $S^{5}, S^{3} \times S^{2}$ , $S^{3} \tilde{\times} S^{2}$ or the Wu manifold $SU (3) ∕ SO (3)$ .

Keywords

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

Mathematical Subject Classification 2010

Primary: 53C20

Secondary: 57S25, 51M25

References

Publication

Received: 5 July 2012

Revised: 8 November 2013

Accepted: 14 December 2013

Published: 7 July 2014

Proposed: John Lott

Seconded: Tobias Colding, Gang Tian

Authors

Fernando Galaz-Garcia
Mathematisches Institut Westfälische Wilhelms-Universität Münster Einsteinst. 62 D-48149 Münster Germany
http://wwwmath.uni-muenster.de/u/fernando.galaz-garcia/
Catherine Searle
Department of Mathematics Oregon State University 368 Kidder Hall Corvallis, Oregon 97331 USA
https://sites.google.com/site/catherinesearle1/home

Volume 18, issue 3 (2014)