Special Kähler-Ricci potentials and Ricci solitons
| dc.creator | Maschler, Gideon | |
| dc.date | 2007-08-08 | |
| dc.date.accessioned | 2026-07-07T08:22:45Z | |
| dc.date.available | 2026-07-07T08:22:45Z | |
| dc.description | On a manifold of dimension at least six, let $(g,τ)$ be a pair consisting of a Kähler metric g which is locally Kähler irreducible, and a nonconstant smooth function $τ$. Off the zero set of $τ$, if the metric $\hat{g}=g/τ^2$ is a gradient Ricci soliton which has soliton function $1/τ$, we show that $\hat{g}$ is Kähler with respect to another complex structure, and locally of a type first described by Koiso. Moreover, $τ$ is a special Kähler-Ricci potential, a notion defined in earlier works of Derdzinski and Maschler. The result extends to dimension four with additional assumptions. We also discuss a Ricci-Hessian equation, which is a generalization of the soliton equation, and observe that the set of pairs $(g,τ)$ satisfying a Ricci-Hessian equation is invariant, in a suitable sense, under the map $(g,τ)\to (\hat{g},1/τ)$. | |
| dc.description | 13 pages, corrected Report-no | |
| dc.identifier | https://arxiv.org/abs/0708.1047 | |
| dc.identifier | http://arxiv.org/abs/0708.1047 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/135756 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C25 (Primary), 53B20, 53B35, 53C55 (Secondary) | |
| dc.title | Special Kähler-Ricci potentials and Ricci solitons | |
| dc.type | text |