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....
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| Autores principales: | , |
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| Formato: | article |
| Lenguaje: | Inglés |
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2022
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| Acceso en línea: | http://hdl.handle.net/11086/30058 https://doi.org/10.48550/arXiv.1210.3656 |
| Aporte de: |
| Sumario: | 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. |
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