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arXiv · 2509.24155

The dual foliation of polar actions on nonnegatively curved manifolds

Yi Shi
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Abstract

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.

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Yi Shi. 2025-09-29. The dual foliation of polar actions on nonnegatively curved manifolds. https://arxiv.org/abs/2509.24155

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