On homogeneous Ricci solitons
We study the evolution of homogeneous Ricci solitons under the bracket flow, a dynamical system on the space Hq,n ⊂ Λ2g∗ ⊗ g of all homogeneous spaces of dimension n with a q-dimensional isotropy, which is equivalent to the Ricci flow for homogeneous manifolds. We prove that algebraic solitons (i.e....
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | article |
| Lenguaje: | Inglés |
| Publicado: |
2022
|
| Materias: | |
| Acceso en línea: | http://hdl.handle.net/11086/30058 https://doi.org/10.48550/arXiv.1210.3656 |
| Aporte de: |
| id |
I10-R141-11086-30058 |
|---|---|
| record_format |
dspace |
| institution |
Universidad Nacional de Córdoba |
| institution_str |
I-10 |
| repository_str |
R-141 |
| collection |
Repositorio Digital Universitario (UNC) |
| language |
Inglés |
| topic |
Soliton |
| spellingShingle |
Soliton Lafuente, Ramiro Augusto Lauret, Jorge Rubén On homogeneous Ricci solitons |
| topic_facet |
Soliton |
| description |
We study the evolution of homogeneous Ricci solitons under the bracket flow, a dynamical system on the space Hq,n ⊂ Λ2g∗ ⊗ g of all homogeneous spaces of dimension n with a q-dimensional isotropy, which is equivalent to the Ricci flow for homogeneous manifolds. We prove that algebraic solitons (i.e. the Ricci operator is a multiple of the identity plus a derivation) are precisely the fixed points of the system, and that a homogeneous Ricci soliton is isometric to an algebraic soliton if and only if the corresponding bracket flow solution is not chaotic, in the sense that its ω-limit set consists of a single point. We also geometrically characterize algebraic solitons among homogeneous Ricci solitons as those for which the Ricci flow solution is simultaneously diagonalizable. |
| format |
article |
| author |
Lafuente, Ramiro Augusto Lauret, Jorge Rubén |
| author_facet |
Lafuente, Ramiro Augusto Lauret, Jorge Rubén |
| author_sort |
Lafuente, Ramiro Augusto |
| title |
On homogeneous Ricci solitons |
| title_short |
On homogeneous Ricci solitons |
| title_full |
On homogeneous Ricci solitons |
| title_fullStr |
On homogeneous Ricci solitons |
| title_full_unstemmed |
On homogeneous Ricci solitons |
| title_sort |
on homogeneous ricci solitons |
| publishDate |
2022 |
| url |
http://hdl.handle.net/11086/30058 https://doi.org/10.48550/arXiv.1210.3656 |
| work_keys_str_mv |
AT lafuenteramiroaugusto onhomogeneousriccisolitons AT lauretjorgeruben onhomogeneousriccisolitons |
| bdutipo_str |
Repositorios |
| _version_ |
1764820392943288323 |