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...

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Detalles Bibliográficos
Autores: Carmona Jiménez, J. L., Castrillón López, Marco
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
Descripción
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.