The dual foliation of polar actions on nonnegatively curved manifolds

We prove that any dual leaf $L^{\mathrm{\#}}$ of a simply connected, complete nonnegatively curved polar manifold $M$ is totally geodesic and closed in $M$, and $L^{\mathrm{\#}}$ is itself a complete nonnegatively curved polar manifold. Furthermore, the dual foliation on $M$ induces a Riemannian submersion with totally geodesic fibers from $M$ to a homogeneous space.