On Ricci Solitons with Isoparametric Potential Functions
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866912839312080896 |
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| author | Tran, Hung Yamazaki, Kazuo |
| author_facet | Tran, Hung Yamazaki, Kazuo |
| contents | This paper studies a complete gradient Ricci soliton with an isoparametric potential function. Our first theorem asserts that, for the steady case, there is a critical level set of codimension greater than one. This is consistent with construction of cohomogeneity one models with singular orbits. There is a partial result for the shrinking case. We also study a particular ansatz of popular interest and obtain asymptotic behaviors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_03545 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Ricci Solitons with Isoparametric Potential Functions Tran, Hung Yamazaki, Kazuo Differential Geometry Primary 53E20, 53C25, Secondary 53C22 This paper studies a complete gradient Ricci soliton with an isoparametric potential function. Our first theorem asserts that, for the steady case, there is a critical level set of codimension greater than one. This is consistent with construction of cohomogeneity one models with singular orbits. There is a partial result for the shrinking case. We also study a particular ansatz of popular interest and obtain asymptotic behaviors. |
| title | On Ricci Solitons with Isoparametric Potential Functions |
| topic | Differential Geometry Primary 53E20, 53C25, Secondary 53C22 |
| url | https://arxiv.org/abs/2506.03545 |