The Ambrose-Singer theorem for cohomogeneity one Riemannian manifolds

We characterize regular isometric actions whose principal orbits are hypersurfaces through the existence of a linear connection satisfying a set of covariant equations in the same spirit as the Ambrose-Singer Theorem for homogeneous spaces. These results are then used to describe isometric cohomogen...

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Detalhes bibliográficos
Autores: Carmona Jiménez, José Luis, Castrillón López, Marco, Díaz Ramos, José Carlos
Formato: artículo
Fecha de publicación:2025
País:España
Recursos:Universidad de Santiago de Compostela (USC)
Repositorio:Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
Idioma:inglés
OAI Identifier:oai:minerva.usc.gal:10347/43989
Acesso em linha:https://hdl.handle.net/10347/43989
Access Level:acceso abierto
Palavra-chave:Ambrose-Singer theorem
Cohomogeneity one actions
Canonical connection
12 Matemáticas
Descrição
Resumo:We characterize regular isometric actions whose principal orbits are hypersurfaces through the existence of a linear connection satisfying a set of covariant equations in the same spirit as the Ambrose-Singer Theorem for homogeneous spaces. These results are then used to describe isometric cohomogeneity one foliations in terms of such connections. Finally, we provide explicit examples of these objects in Euclidean spaces and real hyperbolic spaces.