LOW-DIMENSIONAL MANIFOLDS WITH NON-NEGATIVE CURVATURE AND MAXIMAL SYMMETRY RANK

We classify closed, simply connected n-manifolds of non-negative sectional curvature admitting an isometric torus action of maximal symmetry rank in dimensions 2 <= n <= 6. In dimensions 3k, k = 1,2 there is only one such manifold and it is diffeomorphic to the product of k copies of the 3-sphere.