Non-negatively curved 5-manifolds with almost maximal symmetry rank

TL;DR

This paper classifies certain 5-dimensional manifolds with non-negative curvature and symmetry, showing they are diffeomorphic to well-known spaces like spheres, products, or specific bundles.

Contribution

It provides a complete classification of closed, simply-connected, non-negatively curved 5-manifolds with an effective $T^2$ symmetry.

Findings

Identifies four diffeomorphism types of such manifolds.

Shows these manifolds are either spheres, products, or specific bundles.

Establishes a link between symmetry rank and manifold topology.

Abstract

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