The homogeneous geometries of complex hyperbolic space
We describe the holonomy algebras of all canonical connections and their action on complex hyperbolic spaces CH(n) in all dimensions (n ∈ N). This thorough investigation yields a formula for all Kähler homogeneous structures on complex hyperbolic spaces. Finally, we have related the belonging of the...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/7226 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/7226 |
| Access Level: | acceso abierto |
| Palabra clave: | 514.7 Canonical connection Complex hyperbolic space Homogeneous structures Holonomy Geometría diferencial 1204.04 Geometría Diferencial |
| Sumario: | We describe the holonomy algebras of all canonical connections and their action on complex hyperbolic spaces CH(n) in all dimensions (n ∈ N). This thorough investigation yields a formula for all Kähler homogeneous structures on complex hyperbolic spaces. Finally, we have related the belonging of the homogeneous structures to the different Tricerri and Vanhecke’s (or Abbena and Garbiero’s) orthogonal and irreducible U(n)-submodules with concrete and determined expressions of the holonomy. |
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