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Métricas de Einstein en grupos de Lie lorentzianos
- Autor/a
- Otero Casal, Tomás
The goal of this work is to study the existence of left-invariant Einstein Lorentzian metrics in 4-dimensional Lie groups. For this purpose, we use the correspondence between left-invariant metrics on Lie groups and inner products in their Lie algebras in order to work with them at the algebraic level. We give a complete classification of Einstein metrics on 4-dimensional Lorentzian Lie gropus and analyze the geometry of the different examples. The only non-symmetric examples correspond to Ricci-flat plane waves and three homothetic classes of Lie groups with left-invariant Lorentzian metrics.
Ficha técnica
- Edición
- 1
- Lugar de publicación
- Santiago de Compostela
- Año publicación
- 2023
- Serie
- 152b Publicaciones del Departamento de Geometría y Topología
- Disponibilidad
- Si
The goal of this work is to study the existence of left-invariant Einstein Lorentzian metrics in 4-dimensional Lie groups. For this purpose, we use the correspondence between left-invariant metrics on Lie groups and inner products in their Lie algebras in order to work with them at the algebraic level. We give a complete classification of Einstein metrics on 4-dimensional Lorentzian Lie gropus and analyze the geometry of the different examples. The only non-symmetric examples correspond to Ricci-flat plane waves and three homothetic classes of Lie groups with left-invariant Lorentzian metrics.