Carmona Jiménez, José LuisCastrillón López, MarcoDíaz Ramos, José Carlos2025-11-242025-11-242025-07-23Carmona Jiménez, J.L., Castrillón López, M. & Díaz-Ramos, J.C. The Ambrose-Singer Theorem for Cohomogeneity One Riemannian Manifolds. Transformation Groups (2025). https://doi.org/10.1007/s00031-025-09927-x1083-4362https://hdl.handle.net/10347/43989We 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.engThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licen ses/by/4.0Attribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/Ambrose-Singer theoremCohomogeneity one actionsCanonical connection12 Matemáticasjournal article10.1007/s00031-025-09927-x1531-586Xopen access