Dual leaves of polar actions on simply connected complete nonnegatively curved manifolds are totally geodesic and closed, themselves polar and nonnegatively curved, inducing a Riemannian submersion to a homogeneous space.
Kollross, Polar actions on symmetric spaces, Journal of Differential Geometry, 77, 425–482 (2009)
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The dual foliation of polar actions on nonnegatively curved manifolds
Dual leaves of polar actions on simply connected complete nonnegatively curved manifolds are totally geodesic and closed, themselves polar and nonnegatively curved, inducing a Riemannian submersion to a homogeneous space.