Carmona Jiménez, José LuisCastrillón López, Marco2025-12-022025-12-022022Carmona Jiménez, J.L., Castrillón López, M. The Ambrose–Singer Theorem for General Homogeneous Manifolds with Applications to Symplectic Geometry. Mediterr. J. Math. 19, 280 (2022).10.1007/s00009-022-02197-xhttps://hdl.handle.net/20.500.14352/1283412022 Acuerdos transformativos CRUEThe main Theorem of this article provides a characterization of reductive homogeneous spaces equipped with some geometric structure (not necessarily pseudo-Riemannian) in terms of the existence of certain connection. This result generalizes the well-known Theorem of Ambrose and Singer for Riemannian homogeneous spaces (Ambrose and Singer in Duke Math J 25(4):647–669, 1958). We relax the conditions in this theorem and prove a characterization of reductive locally homogeneous manifolds. Finally, we apply these results to classify, with explicit expressions, reductive locally homogeneous almost symplectic, symplectic and Fedosov manifolds.engAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/journal articlehttps://doi.org/10.1007/s00009-022-02197-xhttps://arxiv.org/abs/2001.06254open accessAmbrose–Singer theoremCanonical connectionFedosov manifoldsHomogeneous manifoldsHomogeneous structuresLocally homogeneous manifoldsSymplectic manifoldsCiencias12 Matemáticas