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...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/132710 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/132710 |
| Access Level: | acceso abierto |
| Palabra clave: | Ambrose-Singer theorem Canonical connection Cohomogeneity one actions Geometría diferencial 1204.04 Geometría Diferencial |
| Sumario: | 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. |
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