  Polar manifolds are Riemannian G-manifolds admitting a "section", i.e., a
complete submanifold passing through every orbit and doing so orthogonally. We
consider compact simply-connected polar manifolds and achieve an equivariantly
diffeomorphic classification in dimensions 5 or less. As an application, we
determine which of these polar actions admit an invariant metric with
non-negative curvature.
