Some Remarks on Isoparametric Functions in Closed 4-Manifolds
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913697953218560 |
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| author | Li, Minghao |
| author_facet | Li, Minghao |
| contents | We study transnormal and isoparametric functions on closed Riemannian 4-manifolds and establish fundamental restrictions on their topology and geometry. In particular, we show that such manifolds cannot be endowed with negatively curved metrics, contrasting with known results in the compact simply connected case. Moreover, in certain cases, we provide a description of their fundamental groups. These findings contribute to a better understanding of the global structure of isoparametric foliations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_12563 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some Remarks on Isoparametric Functions in Closed 4-Manifolds Li, Minghao Geometric Topology Differential Geometry 53C20, 57R30, 53C12, 57K40 We study transnormal and isoparametric functions on closed Riemannian 4-manifolds and establish fundamental restrictions on their topology and geometry. In particular, we show that such manifolds cannot be endowed with negatively curved metrics, contrasting with known results in the compact simply connected case. Moreover, in certain cases, we provide a description of their fundamental groups. These findings contribute to a better understanding of the global structure of isoparametric foliations. |
| title | Some Remarks on Isoparametric Functions in Closed 4-Manifolds |
| topic | Geometric Topology Differential Geometry 53C20, 57R30, 53C12, 57K40 |
| url | https://arxiv.org/abs/2501.12563 |