The Ambrose-Singer theorem for cohomogeneity one Riemannian manifolds
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ISSN: 1083-4362
E-ISSN: 1531-586X
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Abstract
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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Carmona 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-x
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Attribution 4.0 International
Attribution 4.0 International