A rigidity result for axisymmetric toric Ricci solitons
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929573903466496 |
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| author | Zhang, Shiqiao |
| author_facet | Zhang, Shiqiao |
| contents | We examine a non-axisymmetric perturbation of a family of axisymmetric toric Einstein manifolds and Ricci solitons studied in Firester-Tsiamis (2024). We establish a rigidity result stating that these axisymmetric Ricci solitons do not admit constant-angle non-axisymmetric perturbations except for conformally flat cases. For these new cases, our result leads to an explicit description of the Einstein metrics and a classification of the Ricci solitons under a volume-collapsing ansatz. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_00861 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A rigidity result for axisymmetric toric Ricci solitons Zhang, Shiqiao Differential Geometry We examine a non-axisymmetric perturbation of a family of axisymmetric toric Einstein manifolds and Ricci solitons studied in Firester-Tsiamis (2024). We establish a rigidity result stating that these axisymmetric Ricci solitons do not admit constant-angle non-axisymmetric perturbations except for conformally flat cases. For these new cases, our result leads to an explicit description of the Einstein metrics and a classification of the Ricci solitons under a volume-collapsing ansatz. |
| title | A rigidity result for axisymmetric toric Ricci solitons |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2411.00861 |