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

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