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 $2\le n\le 6$. 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.