Kähler-Ricci solitons with almost maximal symmetry
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909010472468480 |
|---|---|
| author | Dung, Ha Tuan Searle, Catherine Tran, Hung |
| author_facet | Dung, Ha Tuan Searle, Catherine Tran, Hung |
| contents | This paper studies a non-trivial gradient Kähler-Ricci soliton, of complex dimension $n$, with an isometry group of dimension at least $n^2-1$. We show that the isometry group acts by cohomogeneity one and, consequently, admits a special ansatz involving a Sasakian model. In complex dimension two, we can actually say more: namely, that every such soliton has maximal symmetry; that is, the isometry group is exactly of dimension $2^2$. In addition, we prove that, if the isometry group acts by cohomogeneity one on a non-trivial gradient Ricci soliton (not necessarily Kähler), the potential function is invariant by the action. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_01557 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Kähler-Ricci solitons with almost maximal symmetry Dung, Ha Tuan Searle, Catherine Tran, Hung Differential Geometry Primary 53C15, 53C25, 53C55, 53E20, 53E30, Secondary 53D15 This paper studies a non-trivial gradient Kähler-Ricci soliton, of complex dimension $n$, with an isometry group of dimension at least $n^2-1$. We show that the isometry group acts by cohomogeneity one and, consequently, admits a special ansatz involving a Sasakian model. In complex dimension two, we can actually say more: namely, that every such soliton has maximal symmetry; that is, the isometry group is exactly of dimension $2^2$. In addition, we prove that, if the isometry group acts by cohomogeneity one on a non-trivial gradient Ricci soliton (not necessarily Kähler), the potential function is invariant by the action. |
| title | Kähler-Ricci solitons with almost maximal symmetry |
| topic | Differential Geometry Primary 53C15, 53C25, 53C55, 53E20, 53E30, Secondary 53D15 |
| url | https://arxiv.org/abs/2605.01557 |