Nonnegatively curved 5–manifolds with almost maximal symmetry rank

Galaz-Garcia, Fernando¹ ; Searle, Catherine²

¹ Mathematisches Institut, Westfälische Wilhelms-Universität Münster, Einsteinst. 62, D-48149 Münster, Germany
² Department of Mathematics, Oregon State University, 368 Kidder Hall, Corvallis, Oregon 97331, USA

Geometry & topology, Tome 18 (2014) no. 3, pp. 1397-1435.

Résumé

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 $\mathit{SU}\left(3\right)∕\mathit{SO}\left(3\right)$.

Détail

DOI : 10.2140/gt.2014.18.1397

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

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