Toral symmetries of collapsed ancient solutions to the homogeneous Ricci flow
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866911461593317376 |
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| author | Krishnan, Anusha M. Pediconi, Francesco Sbiti, Sammy |
| author_facet | Krishnan, Anusha M. Pediconi, Francesco Sbiti, Sammy |
| contents | Collapsed ancient solutions to the homogeneous Ricci flow on compact manifolds occur only on the total space of principal torus bundles. Under an algebraic assumption that guarantees flowing through diagonal metrics and a tameness assumption on the collapsing directions, we prove that such solutions have additional symmetries, i.e., they are invariant under the right action of their collapsing torus. As a byproduct of these additional torus symmetries, we prove that these solutions converge, backward in time, in the Gromov-Hausdorff topology to an Einstein metric on the base of a torus bundle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_01469 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Toral symmetries of collapsed ancient solutions to the homogeneous Ricci flow Krishnan, Anusha M. Pediconi, Francesco Sbiti, Sammy Differential Geometry 53C30, 53C21, 53E20, 57S15 Collapsed ancient solutions to the homogeneous Ricci flow on compact manifolds occur only on the total space of principal torus bundles. Under an algebraic assumption that guarantees flowing through diagonal metrics and a tameness assumption on the collapsing directions, we prove that such solutions have additional symmetries, i.e., they are invariant under the right action of their collapsing torus. As a byproduct of these additional torus symmetries, we prove that these solutions converge, backward in time, in the Gromov-Hausdorff topology to an Einstein metric on the base of a torus bundle. |
| title | Toral symmetries of collapsed ancient solutions to the homogeneous Ricci flow |
| topic | Differential Geometry 53C30, 53C21, 53E20, 57S15 |
| url | https://arxiv.org/abs/2312.01469 |