Carmona Jiménez, José LuisCastrillón López, MarcoDíaz Ramos, José Carlos2026-02-192026-02-192025Carmona Jiménez, J.L., Castrillón López, M. & Díaz-Ramos, J.C. The Ambrose-Singer Theorem for Cohomogeneity One Riemannian Manifolds. Transformation Groups. 20251083-43621531-586X10.1007/s00031-025-09927-xhttps://hdl.handle.net/20.500.14352/1327102025 Acuerdos Transformativos CRUEWe 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.engAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/journal articleopen accessAmbrose-Singer theoremCanonical connectionCohomogeneity one actionsGeometría diferencial1204.04 Geometría Diferencial