This paper shows that dual leaves are closed and totally geodesic in nonnegatively curved polar manifolds, implying Riemannian structures.
We prove that any dual leaf L# of a simply connected, complete nonnegatively curved polar manifold M is totally geodesic and closed in M, and L# 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.
No takes yet. Share an insight, caveat, or question.
Yi Shi (2025) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: