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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.24155 |
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| _version_ | 1866908958732582912 |
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| author | Shi, Yi |
| author_facet | Shi, Yi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_24155 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The dual foliation of polar actions on nonnegatively curved manifolds Shi, Yi Differential Geometry 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. |
| title | The dual foliation of polar actions on nonnegatively curved manifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2509.24155 |