On homogeneous Ricci solitons
We study the evolution of homogeneous Ricci solitons under the bracket flow, a dynamical system on the space Graphic 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 Ric...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2013 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/8499 |
| Acceso en línea: | http://hdl.handle.net/11336/8499 |
| Access Level: | acceso abierto |
| Palabra clave: | Soliton https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | We study the evolution of homogeneous Ricci solitons under the bracket flow, a dynamical system on the space Graphic 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. |
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