A remark on Ricci flow of left invariant metrics
| dc.creator | Arteaga, J. A. | |
| dc.creator | Malakhaltsev, M. A. | |
| dc.date | 2005-07-22 | |
| dc.date | 2005-07-27 | |
| dc.date.accessioned | 2026-07-07T05:21:56Z | |
| dc.date.available | 2026-07-07T05:21:56Z | |
| dc.description | We prove that the Ricci flow equation for left invariant metrics on Lie groups reduces to a first order ordinary differential equation for a map $Q : (-a,a) \to UT$, where $UT$ is the group of upper triangular matrices. We decompose the matrix $R_{ij}$ of Ricci tensor coordinates with respect to an orthonormal frame field $E_{i}$ into a sum $\overset{1}{R}_{ij} + \overset{2}{R}_{ij} + \overset{3}{R}_{ij} + \overset{4}{R}_{ij}$ such that, for any $E_{i'} = U^i_{i'} E_i$ with $||U^i_{i'}|| \in O(n)$, $\oversetα{R}_{i'j'} = U_{i'}^i \oversetα{R}_{ij} U^j_{j'}$. This allows us to specify several cases when the differential equation can be simplified. As an example we consider three-dimensional unimodular Lie groups. | |
| dc.description | Paper is replaced because of some typos in formulas (especially in part II) | |
| dc.identifier | https://arxiv.org/abs/math/0507473 | |
| dc.identifier | http://arxiv.org/abs/math/0507473 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75875 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C21; 53C25; 53C30 | |
| dc.title | A remark on Ricci flow of left invariant metrics | |
| dc.type | text |