The Existence of Soliton Metrics for Nilpotent Lie Groups
| dc.creator | Payne, Tracy L. | |
| dc.date | 2008-09-29 | |
| dc.date.accessioned | 2026-07-07T10:06:20Z | |
| dc.date.available | 2026-07-07T10:06:20Z | |
| dc.description | We show that a left-invariant metric g on a nilpotent Lie group N is a soliton metric if and only if a matrix U and vector v associated the manifold (N,g) satisfy the matrix equation Uv = [1], where [1] is a vector with every entry a one. We associate a generalized Cartan matrix to the matrix U and use the theory of Kac-Moody algebras to analyze the solution spaces for such linear systems. We use these methods to find infinitely many new examples of nilmanifolds with soliton metrics. We give a sufficient condition for a sum of soliton metric nilpotent Lie algebra structures to be soliton, and we use this criterion to show that soliton metrics exist on every naturally graded filiform metric Lie algebra. | |
| dc.description | 47 pages | |
| dc.identifier | https://arxiv.org/abs/0809.5068 | |
| dc.identifier | http://arxiv.org/abs/0809.5068 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/170291 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C25 (Primary) 53C30, 22E25, 22F30 (Secondary) | |
| dc.title | The Existence of Soliton Metrics for Nilpotent Lie Groups | |
| dc.type | text |