%0 Journal Article
%A Carmona Jiménez, José Luis
%A Castrillón López, Marco
%T The Ambrose-Singer Theorem for general homogeneous manifolds with applications to symplectic geometry
%D 2022
%U https://hdl.handle.net/20.500.14352/128341
%X The 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.
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