The Equivalence of the Existences of Transnormal and Isoparametric Functions on Compact Manifolds
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913691996258304 |
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| author | Li, Minghao Yang, Ling |
| author_facet | Li, Minghao Yang, Ling |
| contents | Through exploring the embedded transnormal systems of codimension 1, we show the existence of a transnormal function on a connected complete Riemannian manifold requires the underlying manifold to have a vector bundle structure or a linear double disk bundle decomposition. Conversely, any smooth manifold with either of these structures can be endowed with a Riemannian metric so that it admits a transnormal function, which, under suitable compactness conditions, can become isoparametric. As a corollary, for compact manifolds, the existences of transnormal and isoparametric functions impose the same topological constraints. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_21016 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Equivalence of the Existences of Transnormal and Isoparametric Functions on Compact Manifolds Li, Minghao Yang, Ling Differential Geometry 53C12, 53C40, 57R30 Through exploring the embedded transnormal systems of codimension 1, we show the existence of a transnormal function on a connected complete Riemannian manifold requires the underlying manifold to have a vector bundle structure or a linear double disk bundle decomposition. Conversely, any smooth manifold with either of these structures can be endowed with a Riemannian metric so that it admits a transnormal function, which, under suitable compactness conditions, can become isoparametric. As a corollary, for compact manifolds, the existences of transnormal and isoparametric functions impose the same topological constraints. |
| title | The Equivalence of the Existences of Transnormal and Isoparametric Functions on Compact Manifolds |
| topic | Differential Geometry 53C12, 53C40, 57R30 |
| url | https://arxiv.org/abs/2410.21016 |