Volume 18, issue 3 (2014)

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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
Abstract

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

Keywords
symmetry rank, nonnegative curvature, $5$–manifold, torus action
Mathematical Subject Classification 2010
Primary: 53C20
Secondary: 57S25, 51M25